Question

find the derivative of f(x) = 9e^x + x^5. f(x) =

Explanation:

Step1: Apply sum - rule of derivatives

The derivative of a sum $u + v$ is $u'+v'$. So $f'(x)=(9e^{x})'+(x^{5})'$.

Step2: Differentiate $9e^{x}$

The derivative of $ae^{x}$ (where $a$ is a constant) is $ae^{x}$. So $(9e^{x})' = 9e^{x}$.

Step3: Differentiate $x^{5}$

Using the power - rule $(x^{n})'=nx^{n - 1}$, for $n = 5$, we have $(x^{5})'=5x^{4}$.

Answer:

$9e^{x}+5x^{4}$