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The function f(x)=e^x+x , being differen...

The function `f(x)=e^x+x ,` being differentiable and one-to-one, has a differentiable inverse `f^(-1)(x)dot` The value of `d/(dx)(f^(-1))` at the point `f(log2)` is `1/(1n2)` (b) `1/3` (c) `1/4` (d) none of these

A

`(1)/(In2)`

B

`(1)/(3)`

C

`(1)/(4)`

D

none of these

Text Solution

Verified by Experts

`"Let "g(x)=f^(-1)(x)thereforef(g(x))=x`
`"or "f'(g(x))g'(x)=1`
`"or "(e^(g(x))+1)g'(x)=1`
`"or "(e^(g(f(log 2)))+1)g'(f(log 2))=1`
`"or "(e^(log2)+1)g'(f(log 2))=1`
`"or "g'(f(log 2))=1//3`
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CENGAGE-DIFFERENTIATION-Exercise (Single)
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  7. If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s x/(2y-1)...

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  14. If y=(x^x) then (dy)/(dx) is

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  15. The first derivative of the function [cos^(-1)(s insqrt((1+x)/2))+x^x]...

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  19. Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f prime prime(x...

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