How do you find the derivative of $y = 6 cos (x^{2})$ $y= 6cos(x^2)$ ?

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Answer 1 · 2014-09-07T15:11:03

By Chain Rule, $y'=-12sin(x^2)$ .

Recall: Chain Rule
$[f(g(x))]'=f'(g(x))cdot g'(x)$

In the posted function,
$f(x)=6cos x$ and $g(x)=x^2$
By taking the derivative,
$f'(x)=-6sin x$ and $g'(x)=2x$

Now, we have
$y'=-6sin(x^2)cdot 2x=-12sin(x^2)$

How do you find the derivative of y= 6cos(x^2)y=6cos(x2)y= 6cos(x^2) ?