Differentiate sin2 x w.r.t. ecos x. - Vidyadip

Question

Differentiate sin² x w.r.t. e^{cos x}.

✓

Answer

Let u (x) = sin² 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}
$\therefore$ $\frac{d u}{d v}=\frac{2 \sin x \cos x}{-\sin x e^{\cos x}}=-\frac{2 \cos x}{e^{\cos x}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks" from Continuity and Differentiability→Continuity and Differentiability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following integrals:
$\int\limits^{4}_2\frac{\text{x}}{\text{x}^2+1}\text{dx}$

Write a value of $\int\cos^4\text{x }\sin\text{x}\text{ dx}$

Evaluate the following integrals:
$\int\limits^\frac{\pi}{4}_0\sin2\text{x dx}$

If A and B are square matrices of order 3 such that |A| = – 1, |B| = 3, then find the value of |2AB|.

Write two different vectors having same magnitude.

Write the primitive or anti-derivative of $\text{f(x)}=\sqrt{\text{x}}=\frac{1}{\sqrt{\text{x}}}$.

Write a value of $\int\sin^3\text{x}\cos\text{x dx}$

Evaluate the following:
$\sec^{-1}\Big\{\sec\Big(-\frac{7\pi}{3}\Big)\Big\}$

Write the identity element for the binary operation * defined on the set R of all real numbers by the rule $\text{a}\times\text{b}=\frac{3\text{ab}}{7}\ \forall\text{ a, b}\in\text{R}$.

Prove that if $A$ and $B$ are two independent events, then $A ^{\prime}$ and $B ^{\prime}$ will also be independent.