A) \[2{{e}^{2}}\]
B) 4e
C) 2e
D) \[4{{e}^{2}}\]
Correct Answer: B
Solution :
\[\frac{f'(x)}{f(x)}=1\] \[\forall \,x\,\in \,R\] |
Integrate and use f(1) = 2 |
\[f(x)=2{{e}^{x-1}}\]\[\Rightarrow \]\[f'(x)=2{{e}^{x-1}}\] |
\[h(x)=f(x)\]\[\Rightarrow \]\[h'(x)=f'(x)=f'(f(x))f'(x)\] |
\[h'(1)=f'(f(1))f(1)\] |
\[=f'(2)f'(1)\] |
= 2e.2 = 4e. |
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