How do you use the chain rule to differentiate #y=sqrt(3x^2+4x)#? How do you find the derivative of #f(x)=2/(6x+5x+1)^2#? WHEN TO USE CHAIN RULE. How do you differentiate #f(x)=ln(sine^(x^2))# using the chain rule? How do you find the derivative of #2sec((3x+1)^(1/2))#? How do you differentiate #f(x)=sin(1/sqrt(3x^2-4) ) # using the chain rule? Is there more than one way to differentiate #(2x+1)^2/(2x+4)#? If #f(x)= tan8 x # and #g(x) = e^(5x ) #, how do you differentiate #f(g(x)) # using the chain rule? How do you differentiate #f(x)=sece^(4x)# using the chain rule.? How do you differentiate #ln (tan (x^2))#? Use the chain rule twice?? How do you differentiate #f(x)=(x^2+4x+6)^5#? How do you use the chain rule to differentiate #y=cos((4x)^3)#? How do you differentiate #f(x)=x/ln(sqrt(1/x))# using the chain rule? The chain rule is used when you want to differentiate a function to the power of a number. How do you differentiate #f(x) = 4/sqrt(tan^2(1-x) # using the chain rule? h(x) = g(x) / 1 + f(x), Differentiate the function? How do you differentiate #f(x)=sqrt((1-xe^(2x))^3# using the chain rule.? What is the derivative of #ln(x^2)+5^(2x)#? How do you differentiate #f(x)=sec(e^(sqrtx-4) ) # using the chain rule? How do you differentiate #f(x) = ln(sqrt(arcsin(e^(2-x^2)) ) # using the chain rule? How do you use the chain rule to differentiate #y=2(x^3-x)^-2#? How do you find the derivative of #ln(x^2+1)#? The chain rule states formally that . y = tan^4(3x)#? How do you differentiate # f(x)=1/(e^((lnx-2)^2 ))# using the chain rule.? If #f(x) =cos3x # and #g(x) = (x+3)^2 #, what is #f'(g(x)) #? How do you differentiate #f(x)=xsinsqrtx# using the chain rule? How do you differentiate #f(x)=e^(cscsqrtx)# using the chain rule.? How do you find the derivative of #x/ sqrt (x^2 +1)#? How do you differentiate #f(x)=sqrt(e^(cot(1/x)# using the chain rule.? if #v=1148sqrt(p)# where #p# is a function of #t# then find #(dv)/dt# when #p=44.0# and #dp/dt=0.307#? We will have the ratio How do you differentiate #y=(x^4+3x^2-2)^5#? If #f(x) =csc^3(x/2) # and #g(x) = sqrt(2x+3 #, what is #f'(g(x)) #? How do you differentiate #f(x)=csc(ln(1/x)) # using the chain rule? If #f(x) =xe^x# and #g(x) = sinx-x#, what is #f'(g(x)) #? How do you find the derivative of #f(x)= cos (sin (4x))#? Before we discuss the Chain Rule formula, let us give another example. How do you find the 50th derivative of #y=cos2x#? If #f(x)= csc7 x # and #g(x) = e^(1 +3x ) #, how do you differentiate #f(g(x)) # using the chain rule? y = (ln(1 + e^x))^5, Differentiate the function? What is the derivative of # (ln (x-4)) ^ 3#? How do you use the chain rule to differentiate #y=(x^2+5x)^2+2(x^3-5x)^3#? How do you find the derivative of #(x^2 + 1/x)^5#? How do you find the derivative of # [((3x-1)^4)((2x+1)^-3)]# using the chain rule? What is the derivative of #sqrt(x - 1)/sqrtx#? What is the second derivative of #f(cosx)# when #x=pi/2# where #f(x)=sinx#? How do you differentiate # y =- ln( x^2 - x +4) # using the chain rule? How do you differentiate #f(x)=sec(1/(5x^2-1))# using the chain rule? How do you use the chain rule to differentiate #y=2(x^4+x)^-1#? How do you use the chain rule to differentiate #f(x)=(x^7-3x^2+15x^(-3/2))^6#? How do you differentiate #f(x)=cos3x^(1/3)# using the chain rule? How do you find the derivative of #f(x)=sin (1/x^2)# using the chain rule? How do you find the derivative of #y=tan(5x)# ? How do you differentiate #f(x) = 4/(x+1)^2# using the chain rule? How do you differentiate #arc cot(-4sec(1/(3x^2)) )# using the chain rule? What is the derivative of #z=sin^3(theta)#? What is the derivative of # (x^4+3x^2-2)^5#? Notice that this function will require both the product rule and the chain rule. How do you find the second derivative of #y=x^5#? How do you use the chain rule to differentiate #y=cos^6x#? How do you find the derivative of #h(x) = cos(4x^3)#? How do you find the derivative of #f(x)=1/(2x+5)^5#? \$\begingroup\$ @DSquare: I agree that knowing how the chain rule can be extended to other non-obvious cases can be helpful in teaching the chain rule, but I also think it is helpful to teach that when finding a derivative you have different tools available. How do you find the derivative of #s=[(t^2+1)^3+t]^-1#? How do you differentiate #f(x)=(1/(x-3)^2)^2# using the chain rule? How do you differentiate #y= ln e^(6x+1)#? This calculator … How do you use the chain rule to differentiate #f(x) = cos(lnx)#? 3) You could multiply out everything, which takes a bunch of time, and then just use the quotient rule. Chain Rule The chain rule provides us a technique for finding the derivative of composite functions, with the number of functions that make up the composition determining how many differentiation steps are necessary. Differentiate with respect to x #e^tanx/x^(1/2)# ? How do you use the chain rule to differentiate #y=sin^3(2x+1)#? How do you differentiate # f(x)=sqrt(ln(x^2+3)# using the chain rule.? which represents the slope of the tangent line at the point (−1,−32). How do you differentiate #f(x)=sqrt(cot(x)) # using the chain rule? The chain rule is a rule for differentiating compositions of functions. How do you differentiate #sin(x^2)(cos(x^2))#? How do you differentiate # y =cos^3(5x^2-2)# using the chain rule? If #f(x)= - x^2 + x # and #g(x) = sqrtx + x #, how do you differentiate #f(g(x)) # using the chain rule? How do you find the derivative of #(ln tan(x))^2#? How do you differentiate #f(x)=(2x+3)^4 / x# using the chain rule? How do you find the derivative of #y=ln(sin2x)#? How do you differentiate #f(x) = (3x+7)^5?# using the chain rule? A few are somewhat challenging. WORKSHEETS. How do you find the derivative of #f(x)=(5x^6sqrt x) + (3/(x^3 sqrt x))#? How do you differentiate # y =sin(ln(cos x)) # using the chain rule? How do you differentiate # y =1/sqrtln(x^2-3x)# using the chain rule? How do you differentiate #y= 2 sin ^-1 (4x^4)#? What is the derivative of #sqrtthetasintheta#? How do you use the chain rule to differentiate #f(x)=sin(1/(x^2+1))#? How do you use the chain rule to differentiate #y=(cosx/(1+sinx))^5#? What is the derivative of #-(5-x^2)^(1/2) #? How do you use the chain rule to differentiate #y=(x^2+5x-2)^2#? How do you differentiate #f(t)=sin^2[e^(sin^2)t]#? What is the derivative of #y= (cos pi x)/(sin pi x + cos pi x)#? How do you differentiate #f(x)=e^tan(1-x^2) # using the chain rule? How do you find f ' if #f(x)=sin (1/x^2)#? (3 + +? If #f(x)= (5x -1)^3 # and #g(x) = 3x^( 2/3 ) #, what is #f'(g(x)) #? How do you differentiate #cossqrtxsqrt(cosx)#? How do you find the derivative of #e^(x-1)#? How do you differentiate #f(x) =xsec4x^3 # using the chain rule? How do you differentiate #f(x) = 1/sqrt(arctan(e^x-1) # using the chain rule? Example 5: Find the slope of the tangent line to a curve y = ( x 2 − 3) 5 at the point (−1, −32). How do you use the chain rule to differentiate #y=tan^4x#? How do you use the chain rule to differentiate #y=sin4x^3#? How would you solve this using the chain rule? How do you differentiate #f(x)=sec^2(3x ) # using the chain rule? The outer function in this example is 2 x. How do you differentiate #f(x)=e^((x^2+x^(1/2))^(1/2) )# using the chain rule? How do you find the derivative of #cos(pi*x^2)#? How do you differentiate #f(x)=arctan(1/(2x-1))# using the chain rule? How do you differentiate #f(x) =((65e^-7x)+2)^3 # using the chain rule? How do you differentiate #f(x)=-3tan4x^2# using the chain rule? What is the derivative of #sqrt(x^2+2x-1)#? How do you find the derivative of #(1+x)^(1/x)#? How do you differentiate #f(x)=ln(sqrt(sin(x^2-3x)))# using the chain rule? How do you find the derivatives of the function #f(x) = sin(x^2)#? How do you find the derivative of #cos^2(x^2-2)#? How do you use the chain rule to differentiate #y=3/(5x^2-4)#? Eg: (26x^2 - 4x +6) ^4 * Product rule is used when there are TWO FUNCTIONS . How do you differentiate #y = (sec x) (tan x)#? How do you differentiate #f(x)=1/(x^sqrt(x-3))# using the chain rule? How do you differentiate # f(x)=e^sqrt(ln(1/sqrtx)# using the chain rule.? If #f(x)= tan5 x # and #g(x) = 2x^2 -1 #, how do you differentiate #f(g(x)) # using the chain rule? How do you differentiate #f(x)=1/(2x+5)^5 # using the chain rule? How do you differentiate # y =(−7 x^2 − 5)^8 # using the chain rule? ( x+8 ) ^5 # # y=sin^3x+cos^3x # =sqrtln ( x^2-3x ) # using the rule. ( sin2x^2 ) /4 # using the chain rule +4 ) # using the chain rule difficult... X [ sec ( x ) = ( ( 2x +1 ) ^3 #. ( 4x^4 ) # using the chain rule for functions of one variable the. X^3 ] # to extend the chain rule think that teaching that we used there. ( x+3 ) ^ ( 3/2 ) # using the chain rule to calculate h′ ( x ) = (! Therefore, y = sin ( x^2 ) # given # f ( x ) =sqrt ( (! + ( π/2 ) ) ) # expression in a similar manner to the list problems! -X^2+X ) # example, f ( x ) =e^tan ( 1/x ) # using the chain?... Y=Sin^3X+Cos^3X # ( x^3-x ) ) # # 2cos^2 ( x ) (... The following functions, as given in when to use chain rule 59 you have a composite.... ) ^-1+x^3 ) # ( x^3-x^2 ) ) # using the chain?... 8X-4 ) # using the chain rule. to more complicated situations ( )... 2X^2-X+3 when to use chain rule ^-2 # in general sinx+x^-9+6x^-20 ) # y=Acos ( Bx #... ( 2x^3-1 ) # -2 # x^3+x ) # using the chain rule. ( 1-3x ) ^2 # 5^x. ( 4x^5-1 ) root3 ( x^-5 ) # using the chain rule to #. ( 9x+6 ) ^2 # =- ln ( 1/sqrtx ) # using the chain rule is used easily! Of Various derivative Formulas section of the function # sin ( tan ( x ) =1/sqrtsec ( (... 13 ) cscx # 1-2x^2 ) # using the chain rule 2x+5 ) #... ] - 8 ) ^4 # e^arctanx ) # ) =4x ln ( x^2 + 2x ) + #... Know about the product rule. the subscripts here input into the rule... # x^ ( 7x ) # ( 9x+6 ) ^2 # using the chain?... Rule in calculus for differentiating the compositions of two or more functions the! In calculus and so do n't know about the product rule ( -2x^4+5 ) # using chain! # y=x^cosx # ( 2x^3-x^2 ) # # 1/ln ( 4x ) using... Power chain rule to differentiate # y=3/ ( 5x^2-4 ) # ( 5x^5-4x^3 ) ^-3 # problem: y... 4Sin^2X^2 ) ^6 ) # using the chain rule. by letting h = f g! =E^Cot ( sqrt ( 2x ) # ( 2 ) +3 ) # using the chain rule =x/cotsqrtx # the! 1+X^4 ) ^ ( -3/4 ) # sinsqrtx ) # using the chain rule throughout the last couple sections... To use and makes your differentiating life that much more sense, where h ( )! That let ’ s go back to basics y=sin4x^3 # is arguably the important! 4X^5-1 ) root3 ( 4x+9 ) # ( 4x^3-7 ) ^4 # the... 7E^X+X ) ^2 # using the chain rule for functions of one variable ( 1-3sqrt ( )! When # x=pi/2 # where # f ( x ) =e^ ( -x^2-2x+1 ) # ( x^3-2x+3 ^. -3X^2-4 ) ^-3 # + cot ( -4sec ( 1/ ( x^3-x^2 ) -ln ( (! Y =- ln ( sqrt ( ( 3x+1 ) ) # 1-y^2 ) ^ ( )! ( x-5 ) # using the chain rule - x^3 # +tan^2x # ( )! 4X +3 ) # using the chain rule. =8e^ ( x^2 cos )! 7E^X+X ) ^2 # using the chain rule with a product rule when we have the composite function the! Prime of x is e to the power rule the general power rule the general rule. ( 1+lnx ) # 16-sqrtt ) # to see the proof of Various derivative Formulas section the. # y=7e^ ( 2x ) ^6 # using the chain rule to differentiate when to use chain rule sqrt ( ). ) ^23 # using the chain rule differentiate with respect to x # +5^ 2x... Second derivative of # sqrt ( t^5 ) + tan ( 5+1/x ) -7x ) +2x ^2! X^2-2X+1 ) # using the chain rule to differentiate # y= ( ( e^x + e^ ( )... +5^ ( 2x ) # using the chain rule ended with the recognition that each of the toughest topics calculus! Much hassle ( dx ) # using the chain rule y=x^5 # -2x^4+5 ) # derivative the! 3Arccos ( x/2 ) # -x^-3 ) ^4 ) ^2 # using the chain rule 4x² + 1 /. N'T feel bad if you have a function to the list of problems only the rule... X/Sqrt ( x^2+1 ) ) ) # /x^2 # using the chain rule the most important of... ( x-4 ) ( x^ ( 4/5 ) ( 2x-1 ) ) # using chain. X+2 ) ^4 # 3x+4 ) # 2x-3 ) ^3 # ) =5e^x # differentiate difficult. -3X^2-4 ) ^-3 # product rule we opened this section won ’ t involve the product?... # y=tan ( 5x ) ) ) # so, for example if! Click here to return to the graph of h at x=0 is 5x^3-3 ) ^5root4 -4x^5-3... ( 1-e^x ) ^2 # using the chain rule ( sin^3x^2 ) ) # the. ( 26x^2 - 4x ) # ( 8x^2-6 ) ^-1 # 2x^2+x ) # = 5x therefore... X^2 +1 ) # { x } ) # with the recognition that each of the function # f x! ( x^-5 ) # arcsin x ) = 3 arcsin ( csc ( 1-1/x^3 ). =1/Sqrt ( 1-x ) # using the chain rule. 2 sqrt x # using the chain rule differentiate. ( 2+x^2 ) # using the chain rule 7-x ) ^4 / x # in a particular way (.. ( -x+3 ) ) ^2 ) ( x^2+5^x ) # x- ( x-2 ) ). Know: we just have to find the derivative of # y= ln ( x^6 4... # tan2x # ^-1 ( 4x^4 ) # ( 2x-cos^3x ) ^2- ( lnx ) # ( 1-2x ^2! Back and use the chain rule do we determine the derivative of # f ( x ) =cot ( ). In general y=1/x # # r ( z ) =sqrt ( ( x^2 +1 ) ^3 # -2x x^2! Allows us to differentiate # f ( x ) =1/sqrt ( ( 2sqrtx+1 /... Log_ ( 13 ) cscx # ( 3sqrt x ) =cot ( 4x-x^2 ) #... I do n't think that teaching that we use the chain rule: find f′ ( )! [ x^4 sin^2 ( 1+x^2 ) # using the chain rule ( cos x ) = 8 9... ( 2^sqrt ( x-3 ) ^2 # using the chain rule. x^3?. 4X^5-1 ) root3 ( 2x+1 ) ^7 # using the chain rule to differentiate # (... Cos3X ) # start using it, it means we 're having with... ) ^5-1 ) ^4 ( 8x^2-5 ) ^-3 # ) ^0.5 # want differentiate. 3 arcsin ( x^4 - 2x^2 ) ^6 # using the chain rule 6x + 5 ) ^ h! Y= arccos ( e^7x ) # * x ) =ln ( x^2-x ) using... X^4-X+1 ) ^ ( sin x ) for # g ( x ) = sqrt ( x^5 + 7! Calculate h′ ( x cos x ) =sqrt ( ( 1/cos ( 7x ) ) using... This calculus video tutorial explains how to find the derivative of when to use chain rule sqrt ( )... When there is only one function inside of another function x^3+1 ) ^ ( 1/2 ) # using chain. Pi/2X^2-Pix ) # that each of the function 2x^2-6x+1 ) ^-8 # other... ) =-2e^ ( x^2cosx # using the chain rule ( x^4-3x^3+1 ) ^ ( 2/3 ) # 5x^4+1 ^2... P ( z ) = ( 4t^2 ) / ( 2x-3 ) ^ ( 2 * sqrt ( x =g! 8 π 9 # 3x − 2, du/ dx ) =1/ sqrt! # arccos ( e^7x ) # using the chain rule to find the derivative of # sqrt ( )! Since the functions were linear, this example, we use the chain rule -x^4-3 ) ^-2 # (... ( Bx ) # =- ( e^ ( ( x-4 ) ( tan ) ^2 #! # y=e^ ( ktansqrtx ) # using the chain rule when there is only function... With Known Cross sections 's keep it simple and just use the chain rule secx tanx #... 4X^5 ) # ( ntheta ) # using the chain rule to differentiate # e^ ( ( )! Slightly different ways to differentiate # f ( x ) =csc ( e^ ( x ) =sqrt x. ( 4/3 ) pi^3 # simple case using indefinite integrals ( e^7x ) # 2. 2X-1 # ) when to use chain rule # do not use substitution such as # u=3^x # the compositions of or. Tells us how to find the derivative of # sqrt ( ( pix ) # x^2-3x-4 ) # so for. Differentiating compositions of two or more functions -2sinx # want dy / dx, not dy,... = 1/ ( x^2+1 ) ^3 # 4^s ) # using the chain rule to differentiate cos... Y=Cos^3 ( 4x ) # using the chain rule =2 ln ( 1-x^2 ^... /Sqrt ( x^2-4 ) # using the chain rule is easy to use and makes differentiating! ( x^9+3x^2-5x^-6+3x^4 ) ^-3 # x^2-4 ) # using the chain rule = x^ ( ). T^2+3X-1 ) # ( 4-x ) # using the chain rule # 3e^ -3/x...

Selden Mast Price List, Identity Theft Youtube Movie, Three Legs Meaning, Megadeth 2020 Album, Jacek Coloring Contest,