If y = 1 + x y + s i n - 1 s i n 2 x , then d y d x at x = 0 is

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Question: Answered & Verified by Expert

If

y = {(1 + x)}^{y} + s i n^{- 1} (s i n^{2} x)

, then

\frac{d y}{d x}

at

x = 0

is

MathematicsDifferentiationJEE Main

Options:

A $0$
B $\ln 2$
C $1$
D $\frac{1}{2}$

Solution:

1646 Upvotes Verified Answer

The correct answer is:

1

$\frac{d y}{d x} = {(1 + x)}^{y} \{\frac{y}{1 + x} + \ln (1 + x) \cdot \frac{d y}{d x}\} + \frac{s i n 2 x}{\sqrt{1 - s i n^{4} (x)}}$
Putting $x = 0$ & $y = 1$ , we get,

$\frac{d y}{d x} = 1 \{1 + \ln (1) . \frac{d y}{d x}\} + 0 = 1$

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