Continuity and Differentiability — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability2 Marks
Question
Differentiate $\sin^2$ x w.r.t. $e^{\cos x}$.
✓
Answer
Let $u (x) = \sin^2 x$ and $v (x) = e^{\cos x}$ . We want to find $\frac{d u}{d v}=\frac{d u / d x}{d v / d x}$.
Clearly $\frac{d u}{d x} $ = 2 sin x cos x
and $\frac{d v}{d x}$ = $e^{\cos x} (– \sin x) = – (\sin x) e^{\cos x}$
$\therefore$ $\frac{d u}{d v}=\frac{2 \sin x \cos x}{-\sin x e^{\cos x}}=-\frac{2 \cos x}{e^{\cos x}}$
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