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PUNE MCA Exam 2014 Question Paper with answers for online practice

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Question : 10 of 58

Marks: +1, -0

If

e^x

= sinx and 0 < x < π then find

\frac{dy}{dx}

in terms of x

tan x
cot x
-tan x
-cot x

Solution:

Concept:

Implicit differentiation to find

\frac{dy}{dx}

from the given equation.

Explanation:

Given

e^y = \sin x

, differentiate both sides with respect to

x

:

e^y \frac{dy}{dx} = \cos x

.

Thus

\frac{dy}{dx} = \frac{\cos x}{e^y}

.

Since

e^y = \sin x

, substitute:

\frac{dy}{dx} = \frac{\cos x}{\sin x} = \cot x

.

The condition

0 < x < \pi

ensures

\sin x > 0

, so the derivative is defined.

Answer:

\frac{dy}{dx} = \cot x

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