What is the first derivative of cos^3(x^3+13) ?

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We have to find the first derivative of [cos ( x^3 + 13)]^3.

Here we use the chain rule to arrive at the solution.

([cos ( x^3 + 13)]^3 )'

=> 3* [cos ( x^3 + 13)]^2 * [-sin ( x^3 + 13)] * 3x^2

=> -9*x^2* [cos ( x^3 + 13)]^2*sin ( x^3 + 13)

The required derivative of [cos ( x^3 + 13)]^3 is -9*x^2* [cos ( x^3 + 13)]^2*sin ( x^3 + 13)

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