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

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Answer 1 · 2016-10-20T18:59:43

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

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

Using chain rule, $(dy)/(dx)=(dy)/(du)*(du)/(dx)$ , let $u=sin(x)$

$(dy)/(du)=d/(du)cosu=-sinu=-sin(sin(x))$

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

$:.(dy)/(dx)=-sin(sin(x))*cos(x)=-sin(sin(x))cos(x)$

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