A) \[{{e}^{6x}}\sin 6x\]
B) \[2{{e}^{x}}\cos x\]
C) \[8{{e}^{x}}\sin x\]
D) \[8{{e}^{x}}\cos x\]
Correct Answer: B
Solution :
\[f(x)={{e}^{x}}\sin x\] On differentiating w.r.t. x, we get \[f(x)={{e}^{x}}\cos x+\sin x{{e}^{x}}\] Again differentiating, w.r.t. \[x,\]we get \[f\,(x)={{e}^{x}}\cos x-{{e}^{x}}\sin x+{{e}^{x}}\sin x\] \[+\,{{e}^{x}}\cos x\] \[=2{{e}^{x}}\cos x\]
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