Question

Differentiating Exponential functions In Exercise,find the derivative of the function. See Example 2 and 3.

Answer 1

Answer:

$f'(x)=-5ae^{ax}=a f(x)$, where a be a constant.

Step-by-step explanation:

Note: The given functions is a constant function because variable term is missing.

Consider the given function is

$f(x)=-5e^{ax}$

where a be a constant.

We need to find the derivative of the function.

Differentiate with respect to x.

$f'(x)=\dfrac{d}{dx}(-5e^{ax})$

$f'(x)=-5\dfrac{d}{dx}(e^{ax})$

$f'(x)=-5e^{ax}\dfrac{d}{dx}(ax)$            $[\because \dfrac{d}{dx}(e^x)=e^x]$

$f'(x)=-5ae^{ax}$

$f'(x)=a(-5e^{ax})$

$f'(x)=a f(x)$

Therefore, the derivative of the function is $f'(x)=-5ae^{ax}=a f(x)$.