A) \[{f}'({{e}^{x}})\]
B) \[{f}''\,({{e}^{x}})\,{{e}^{x}}+{f}'({{e}^{x}})\]
C) \[{f}''\,({{e}^{x}}){{e}^{2x}}+{f}''({{e}^{x}})\]
D) \[{f}''\,({{e}^{x}}){{e}^{2x}}+{f}'\,({{e}^{x}})\,{{e}^{x}}\]
Correct Answer: D
Solution :
Let \[y=f({{e}^{x}})\] Þ \[\frac{dy}{dx}={f}'({{e}^{x}})\,{{e}^{x}}\] \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={f}''({{e}^{x}}).{{e}^{x}}.{{e}^{x}}+{{e}^{x}}.{f}'({{e}^{x}})\]=\[f''({{e}^{x}}).{{e}^{2x}}+f'({{e}^{x}}).{{e}^{x}}\].
You need to login to perform this action.
You will be redirected in
3 sec
