Question

Differentiate the functions with respect to $x$ in Exercises $1$ to $8$.
$\frac{\sin (ax+b)}{\cos (cx+d)}$

Answer 1

$\frac{d}{dx}\frac{\sin (ax+b)}{\cos (cx+d)}\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{v.\frac{du}{dx}-u\frac{dv}{dx}}{v^2}$

$\frac{a\cos (cx+d)\cos (ax+b)+\sin (ax+b).c.\sin (cx+d)}{{\cos }^2(cx+d)}$

$=\frac{a\cos (cx+d)\cos (ax+b)+c\sin (ax+b)\sin (cx+d)}{{\cos }^2(cx+d)}$