Home › UP Board Class 12 › Mathematics › If $y=e^x+x^e+e^e$, then $\dfrac{dy}{dx}$ equals
If $y=e^x+x^e+e^e$, then $\dfrac{dy}{dx}$ equals
A$e^x+ex^{e-1}$
B$e^x+x^e+e^e$
C$e^x+ex^{e}$
D$e^x+e x^{e-1}+e^e$
Answer & Solution
Correct answer: A. $e^x+ex^{e-1}$
Differentiate term by term. $\dfrac{d}{dx}(e^x)=e^x$, $\dfrac{d}{dx}(x^e)=ex^{e-1}$ because $e$ is a constant, and $\dfrac{d}{dx}(e^e)=0$ since it is a constant. Hence the derivative is $e^x+ex^{e-1}$.
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