How do you differentiate #f(x) = (3x-2)^4# using the chain rule?

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Answer 1 · 2015-11-24T03:03:57

#f'(x)=12(3x-2)^3#

According to the Chain Rule:

#f'(x)=4(3x-2)^3*d/dx[3x-2]#

#f'(x)=4(3x-2)^3*3#

#f'(x)=12(3x-2)^3#

Answer 2 · 2015-11-24T03:11:16

#dy/dx=12(3x-2)^3#

Given -

# y=(3x-2)^4#

Let #U=3x-2#
Then-

#y= U^4#
#dy/(dU)=4U^3#

#(dU)/dx=3#

#dy/d=dy/(dU).(dU)/dx#

#dy/dx=4(U)^3(3)#

#dy/dx=4(3x-2)^3(3)#

#dy/dx=12(3x-2)^3#