Question

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

f(x) = -5e

Answer 1

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

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)=(d)/(dx)(-5e^(ax))`

`f'(x)=-5(d)/(dx)(e^(ax))`

`f'(x)=-5e^(ax)(d)/(dx)(ax)`
`[\because (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)`.