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Let f: (-1,1) rarr R be a differentiabl...

Let `f: (-1,1) rarr R ` be a differentiable function with f(0) = -1 and f'(0) = 1 let g(x) =[f(2f(x)+2)]^2`, then g'(0) =

A

4

B

`-4`

C

log2

D

`-log2`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
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  8. If y = sec(tan^-1x), then dy/dx at x =1 is equal to

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  11. For x in R, f(x) = |log 2 - sin x| and g(x) = f(f(x)), then

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  12. A function f: R rarr R is defined as follows: f(x) = {:{(x,ifxle1),(...

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  15. The funtion f(x) is defined as follows: f(x) = {:{(x^2+ax+b,0lex<2),...

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  16. If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(...

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  17. If x^Y = e^[X - Y], prove that dy/dx= log x/(1+logx)^2.

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  18. If y = e^[ax] sin bx, prove that d^2y/dx^2 - 2a dy/dx +(a^2 + b^2 ) y ...

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