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If for a continuous function `f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x))` , then `y^(prime)(0)` is equal to a. 1 b. 2 c. 0 d. none of these

A

1

B

2

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`y(x)=f(e^(x))e^(f(x))`
`therefore" "y'(x)=f(e^(x)).e^(f(x)).f'(x)+e^(f(x))f'(e^(x)).e^(x)`
`therefore" "y'(0)=f(1).e^(f(0)).f'(0)+e^(f(0))f'(1)`
`=0+e^(0).2=2`
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