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Question

Let f(x) be a polynomial in x. The second derivative of f(ex) at x=1 is

A
ef′′(e)+f(e)
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B
(f′′(e)+f(e))e2
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C
e2f′′(e)
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D
(f′′(e)e+f(e))e
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Solution

The correct option is D (f′′(e)e+f(e))e
Let g(x)=f(ex)
we know (f(g(x)))=f(g(x))×g(x)
First derivative of g(x) =f(ex)ex
Second derivative of g(x) =f′′(ex)e2x+f(ex)ex
g′′(1)=f′′(e)e2+f(e)e

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