What is the derivative of e-e^x+x^e ?

The derivative of e-e^x+x^e is ex^{e-1}-e^x

What is the first derivative of e-e^x+x^e ?

The first derivative of e-e^x+x^e is ex^{e-1}-e^x

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derivative of

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d e}{d x} = 0

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

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

= 0 - e^{x} + e x^{e - 1}

Simplify

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

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