What is the derivative of $cos(sin(x))$ ?

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Answer 1 · 2016-07-07T00:45:31

$d/dx cos(sin(x)) = -cos(x)sin(sin(x))$

The chain rule states that given two functions $f$ and $g$ , we have $(f@g)'(x) = f'(g(x))*g'(x)$ .

In this case, letting $f(x) = cos(x)$ and $g(x) = sin(x)$ , we have

$(f@g)(x) = cos(sin(x))$
$f'(x) = -sin(x)$
$g'(x) = cos(x)$

Thus

$d/dxcos(sin(x)) = (f@g)'(x)$

$= f'(g(x))g'(x)$

$=-sin(sin(x))cos(x)$

What is the derivative of cos(sin(x))cos(sin(x))?