Question

sin(sin x) what is derivative

Answer 1

Explanation:

Proving that the derivative of sin(x) is cos(x) and that the derivative of cos(x) is -sin(x).

Hope it helps you

Answer 2

$\huge\boxed{\red{\rm question}}$

$\rm find \:derivative\:of \:sin(sinx)$

$\huge\boxed{\blue{\rm solution }}$

$\rm let \: the \: value \: of \: sinx \: be \: 'y'$

$\rm equation\: becomes:$

$\boxed{\tt sin(y) }$

$\rm let's \: differentiate \: this \: part$

$\tt \dfrac{d(siny)}{dy}×\dfrac{dsinx}{dx}$

$\rm derivative\: of \: sinx \: is \: cosx$

$\tt cos(y) × cosx$

$\rm replacing \: value \: of \: y$

$\boxed{\tt cos(sinx)(cosx) }$

$\rm thus\: the\: final\: answer\: is\:$

$\tt cos(sinx)×cosx$

additional info:

the derivative of sinx is defined as the cos function of x.