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  • Suppose for a differentiable function ,<img alt="\mathrm{f(0)=0, f(1)=1\: and \: f^{\prime}(0)=4=f^{\p

Suppose for a differentiable function \mathrm{f},\mathrm{f(0)=0, f(1)=1\: and \: f^{\prime}(0)=4=f^{\prime}(1)}. If \mathrm{g(x)=f\left(e^{x}\right) e^{f(x)}\: then \: g^{\prime}(0)} is equal to

Option: 1

4


Option: 2

8


Option: 3

2


Option: 4

none of these


Answers (1)

best_answer

\mathrm{g^{\prime}(x)=f^{\prime}\left(e^{x}\right) e^{x} e^{f(x)}+f\left(e^{x}\right) e^{f(x)} f^{\prime}(x), so \: g^{\prime}(0)=f^{\prime}(1) e^{f(0)}+f(1) e^{f(0)} f^{\prime}(0)=f^{\prime}(1)+f^{\prime}(0)=8}

Posted by

Kuldeep Maurya

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