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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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Answer:

g(f(x)) = 1x² + 1

Step-by-step explanation:

We are given:
f(x) = x² - 1

g(x) = x + 2

And we want to find g(f(x)).

To do this, we substitute f(x) as x in x+2 (the expression that is equal to g(x)), as g(f(x)) is saying that f(x) is the value of x in g(x).

So, this will be:

g(f(x)) = x² - 1 + 2

Simplify

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In your system, place 1 in front of x² - this is the coefficient of x², and also 1 after that - this is a constant.

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<h3>Volume of of cylinder</h3>

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Therefore,

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