What is the derivative of f(x)=e^x+x^e ?

The derivative of f(x)=e^x+x^e is e^x+ex^{e-1}

What is the first derivative of f(x)=e^x+x^e ?

The first derivative of f(x)=e^x+x^e is e^x+ex^{e-1}

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derivative of

f (x) = e^{x} + x^{e}

e^{x} + e x^{e - 1}

Solution steps

\frac{d}{d x} (e^{x} + x^{e})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{x}) + \frac{d}{d x} (x^{e})

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (x^{e}) = e x^{e - 1}

= e^{x} + e x^{e - 1}

What is the derivative of f(x)=e^x+x^e ?
The derivative of f(x)=e^x+x^e is e^x+ex^{e-1}
What is the first derivative of f(x)=e^x+x^e ?
The first derivative of f(x)=e^x+x^e is e^x+ex^{e-1}