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Let f(x) be a polynomial.Then, the secon...

Let `f(x)` be a polynomial.Then, the second order derivative of `f(e^x)` is

A

`f''(e)^(x) *e^(x) + f'(e)^(x)`

B

`f''(e)^(x) *e^(2x) + f'(e)^(x)* e^(2x)`

C

`f''(e)^(x) *e^(2x)`

D

`f''(e)^(x) *e^(2x) + f'((e)^(x))* e^(x)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let ` phi (x) = f(e^(x) )` . Then
`phi'(x) = f'(e^(x)). e^(x)`
` rArr phi''(x)= f''(e^(x)) .e^(x) .e^(x) + f'(e^(x)) . e^(x)`
` = f''(e^(x)) . e^(2x)+ f'(e^(x))e^(x)` .
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 2 (MISCELLANEOUS PROBLEMS)
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