Differentiate each of the following w.r.t. x: (i) e^cot x (ii) e^-sin 2x (iii) e^√(sin x)

Question

Differentiate each of the following w.r.t. x:

(i) e^{cot x}

(ii) e^{-sin 2x}

(iii) e^{\(\sqrt{sin\,\text x}\)}

Answer 1

 (i) y = e^{cot x} z = cot x

Formula :

According to chain rule of differentiation

(ii) Let y = e^{-sin 2x} z = -sin 2x

Formula :

According to chain rule of differentiation

(iii) Let y = e\(^\sqrt{sin\,\text x}\) z = \(\sqrt{sin\,\text x}\)

Formula :

According to chain rule of differentiation