How do you differentiate #f(x)= x^3 (1-3x^2)^4 # using the product rule?

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Answer 1 · 2018-08-12T19:40:05

#f'(x)=3x^2(1-3x^2)^3(1-11x^2)#

Here ,

#f(x)=x^3(1-3x^2)^4#

Diff.w.r.t # x# ,using product rule:

#f'(x)=x^3d/(dx)(1-3x^2)^4+(1-3x^2)^4d/(dx)(x^3)#

Diff.w.r.t. # x# using chain rule:

#f'(x)=x^3 4(1-3x^2)^3(-6x)+(1-3x^2)^4(3x^2)#

#:.f'(x)=(1-3x^2)^3{-24x^4+(1-3x^2)3x^2}#

#:.f'(x)=(1-3x^2)^3{-24x^4+3x^2-9x^4}#

#:.f'(x)=(1-3x^2)^3(3x^2-33x^4)#

#:.f'(x)=3x^2(1-3x^2)^3(1-11x^2)#