What is the derivative of $f (x) = {cos}^{2} (x^{3})$ $f(x)=cos^2(x^3)$ ?

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Answer 1 · 2015-11-16T16:13:32

$f'(x)=-6x^2cos(x^3)sin(x^3)$

$f'(x)=2cos(x^3)d/(dx)[cos(x^3)]$

Now, using the chain rule again, we can find $d/(dx)[cos(x^3)]$ .
$d/(dx)[cos(x^3)]=-sin(x^3)d/(dx)[x^3]=-3x^2sin(x^3)$

So, $f'(x)=2cos(x^3)*-3x^2sin(x^3)=-6x^2cos(x^3)sin(x^3)$

What is the derivative of f(x)=cos^2(x^3)f(x)=cos2(x3)f(x)=cos^2(x^3)?