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

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

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Answer 1 · 2018-06-26T19:19:29

#2x^3*2*cosx^2*-sin(x)^2*2x+cos^2x^2*6x^2#

Explanation:

we have
#f(x)=(2x^3)(cos^2x^2)#
#dy/dx=2x^3*d(cos^2x^2)/dx+(cos^2x^2)*d(2x^3)/dx#

#=>2x^3*2*d(cosx^2)/dx+(cos^2x^2)*2*3*x^2#.....using#[dy/dx=x^n=>nx^(n-1)]#
#=>2x^3*2*(cosx^2)*-sind(x^2)/dx+(cos^2x^2)*6*x^2#
.........using #[dy/dx=cosx=>-sinx]#
#=>2x^3*2*(cosx^2)*-sinx^2*2x+(cos^2x^2)*6*x^2#

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

1 Answer

Explanation:

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