Question

Differentiate the following function: f(x)=e^x+x^e

Answer 1

We need to find derivative of function: $f(x)=e^x+x^e$

There is a sum of two elementary functions - power of x and simple exponential function.

If $e$ is Euler's number, the derivative of $e^x$ is $e^x$. This is a property of the Euler number

And another function is exponentiation, so derivative is

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

Using the summation property, we get answer

$\frac{d}{dx}(f(x))=\frac{d}{dx}(e^x+x^e)=\frac{d}{dx}(e^x)+\frac{d}{dx}(x^e)=e^x+ex^{e-1}$