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MHTCET 11 Apr 2026 Shift 1 Paper

Question : 123 of 150

Marks: +1, -0

y=\sin \left(e^{\log 2 x}\right)

\frac{d y}{d x}

x=\frac{\pi}{2}

Solution:

Concept:

Use the identity

e^{\log a}=a

to simplify the given function before differentiating.

Explanation:

Let

y=\sin\left(e^{\log 2x}\right)

Since

\log

denotes the natural logarithm, the standard result gives

e^{\log 2x}=2x

Therefore, the function simplifies to

y=\sin(2x)

Differentiate both sides with respect to

x

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

Now substitute

x=\frac{\pi}{2}

2\cos\left(2\cdot\frac{\pi}{2}\right)=2\cos\pi

We know

\cos\pi=-1

Hence,

\frac{dy}{dx}=2(-1)=-2

Answer:

The value of

\frac{dy}{dx}

x=\frac{\pi}{2}

-2

, which corresponds to Option B.

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