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UPSC NDA I 2023 Mathematics Solved Paper

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Question : 92 of 120

Marks: +1, -0

What is the derivative of

\sin^2 x

with respect to

\cos^2 x

?

$-1$
1
sin2x
cos2x

Solution:

Concept:

Find the derivative of

\sin^2 x

with respect to

\cos^2 x

.

Explanation:

Let

y = \sin^2 x

and

u = \cos^2 x

.

We need

\frac{dy}{du}

.

Compute

\frac{dy}{dx} = \frac{d}{dx}(\sin^2 x) = 2\sin x \cos x = \sin 2x

.

Compute

\frac{du}{dx} = \frac{d}{dx}(\cos^2 x) = -2\cos x \sin x = -\sin 2x

.

Now

\frac{dy}{du} = \frac{\frac{dy}{dx}}{\frac{du}{dx}} = \frac{\sin 2x}{-\sin 2x} = -1

.

Thus, the derivative is

-1

.

Answer:

Option A:

-1

.

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