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Serjik [45]
3 years ago
13

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

Mathematics
1 answer:
kow [346]3 years ago
6 0

Answer:

f'(x)=3ae^{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)=3e^{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}(3e^{ax})

f'(x)=3\dfrac{d}{dx}(e^{ax})

f'(x)=3e^{ax}\dfrac{d}{dx}(ax)            [\because \dfrac{d}{dx}(e^x)=e^x]

f'(x)=3ae^{ax}

f'(x)=a(3e^{ax})

f'(x)=a f(x)

Therefore, the derivative of the function is f'(x)=3ae^{ax}=a f(x).

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