Answer:
[tex]f'(x)=-5ae^{ax}=a f(x)[/tex], 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
[tex]f(x)=-5e^{ax}[/tex]
where a be a constant.
We need to find the derivative of the function.
Differentiate with respect to x.
[tex]f'(x)=\dfrac{d}{dx}(-5e^{ax})[/tex]
[tex]f'(x)=-5\dfrac{d}{dx}(e^{ax})[/tex]
[tex]f'(x)=-5e^{ax}\dfrac{d}{dx}(ax)[/tex] [tex][\because \dfrac{d}{dx}(e^x)=e^x][/tex]
[tex]f'(x)=-5ae^{ax}[/tex]
[tex]f'(x)=a(-5e^{ax})[/tex]
[tex]f'(x)=a f(x)[/tex]
Therefore, the derivative of the function is [tex]f'(x)=-5ae^{ax}=a f(x)[/tex].
