Let $f(x)=2^{x(x-1)}$ for all $x \geq 1$. Then $\left(f^{-1}\right)^{\prime}(4)$ is $(1 / k) \log _2 e$ where the value of $k$ is

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

Let

f(x)=2^{x(x-1)}

for all

x \geq 1

. Then

\left(f^{-1}\right)^{\prime}(4)

(1 / k) \log _2 e

where the value of

k

View answer and explanation

Correct option: D

Option D (12) is correct. The derivative of the inverse function is calculated and evaluated at x=4, leading to k=12.

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x

y

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x y=1

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[x]

x

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y = {\sec ^{ - 1}}\left[ {\mathrm{cosec}x} \right] + \mathrm{cose}{\mathrm{c}^{ - 1}}\left[ {\sec x} \right] + {\sin ^{ - 1}}[\cos x] + {\cos ^{ - 1}}[\sin x],

\frac{{dy}}{{dx}}

\frac{d}{d x} \sin ^{-1}\left(3 x-4 x^{3}\right)

z = y + f\left( v \right),

v = \left( {\frac{x}{y}} \right),

v\frac{{\partial z}}{{\partial x}} + \frac{{\partial z}}{{\partial y}}