Question

Find $\frac{dy}{dx}$, if $y=\sin (x^2+5)$.

Answer 1

Given $y=\sin (x^2+5)$

$\frac{dy}{dx}=\frac{d\left(\sin (x^2+5)\right)}{dx}$

$x^2+5=u$

$\frac{du}{dx}=2x$

$\frac{dy}{dx}=\frac{d\sin u}{dx}$

$=\cos u\frac{du}{dx}=\cos (x^2+5)\times 2x$

$=2x\cos (x^2+5)$