CBSE Class 12 · 2024 · DifferentiationMultiple Choice

Derivative of

e^{s i n^{2} x}

with respect to

cos x

is:

Answer: (C)

Solution

Let

u = e^{s i n^{2} x}

and

v = cos x

; we need

\frac{d u}{d v} = \frac{d u / d x}{d v / d x}

.
Differentiate

u

by the chain rule:

\frac{d u}{d x} = e^{s i n^{2} x} \cdot 2 sin x cos x

Differentiate

v

\frac{d v}{d x} = - sin x

Divide to get the derivative with respect to

cos x

\frac{d u}{d v} = \frac{e ^{s i n^{2} x} 2 sin x cos x}{- sin x} = - 2 cos x e^{s i n^{2} x}

\frac{d}{d ( cos x )} e^{s i n^{2} x} = - 2 cos x e^{s i n^{2} x}

CBSE Class 12 Board · 2024 · Single correct option