Question

f(x)=cos√sin(tanπx)

Answer 1

$f(x)=cos\sqrt{sin(tan\pi x)}$

Using chain rule of differentiation

$\dfrac{d[f(x)]}{dx}=-sin\sqrt{sin(tan\pi x)}\times\dfrac{1}{2\sqrt{sin(tan\pi x)}}\times cos(tan\pi x)\times sec(2\pi x)\times \pi$

$f'(x)=-\dfrac{\pi \sin\sqrt{\sin(\tan\pi x)}\space \cos(\tan\pi x)\space \sec(2\pi x) }{2\sqrt{\sin(\tan(\pi x))}}$