Question

Differentiate $\cos \left(\sin \right(x^2+x\left)\right)$ with respect to $x$.

Answer 1

The function $f\left(x\right)=\left(\cos \right(\sin (x^2+x))$ is a composition of the three functions.
Hence, by chain rule differentiate w.r.t $x$
$\frac{df\left(x\right)}{dx}=-\sin \left(\sin \right(x^2+x\left)\right)\left(\cos \right(x^2+x\left)\right)(2x+1)$
$=-(2x+1)\left(\cos \right(x^2+x\left)\right)\sin \left(\sin \right(x^2+x\left)\right)$