Let ${e^{f(x)}} = \log x.$ If $g(x)$ is the inverse of $f(x),$ then find $g'(x).$

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

Let

{e^{f(x)}} = \log x.

g(x)

is the inverse of

f(x),

then find

g'(x).

View answer and explanation

Correct option: C

{e^{{e^x} + x}}

Option A (

{e^{{e^x}}}

) is incorrect. Option B (

{e^x}

) is incorrect. Option C (

{e^{{e^x} + x}}

) is correct because it is the derivative of the inverse function g(x) found by using the relationship between f(x) and g(x). Option D (None of these) is incorrect.

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. The minimum value of

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f(x)=[x] \sin (\pi x)

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. Then at

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f(x)

is If

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],

then

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

is equal to

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

is equal to If

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

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

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