What is the derivative of $sin x^2$ ?

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Answer 1 · 2018-04-22T08:54:56

$2xcos(x^2)$

Using the chain rule,

$dy/dx=dy/(du)*(du)/dx$

Let $u=x^2,du=2x \ dx,:.(du)/dx=2x$ .

Then $y=sin(u),dy=cos(u) \ du,:.dy/(du)=cos(u)$ .

Combining, we get,

$dy/dx=cos(u)*2x$

$=2xcos(u)$

Substitute back $u=x^2$ to get the final answer:

$=2xcos(x^2)$

What is the derivative of sin x^2sin x^2?