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

f(x) = -5e

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Answer:


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).

User Angel Yordanov
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