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My name is Ann [436]
3 years ago
5

Differentiating Exponential Functions In Exercise, find the derivative of the function.

Mathematics
1 answer:
Leviafan [203]3 years ago
4 0

Answer:

y' = \frac{1 - 2x}{e^{4x}}

Step-by-step explanation:

If we have a quotient function y, in the following format

y = \frac{f(x)}{g(x)}

This function has the following derivative

y' = \frac{f'(x)*g(x) - g'(x)*f(x)}{(g(x))^{2}}

In this problem, we have that:

f(x) = x, g(x) = e^{2x}

So

f'(x) = 1, g'(x) = 2e^{2x}

The derivative of the function is:

y' = \frac{f'(x)*g(x) - g'(x)*f(x)}{(g(x))^{2}}

y' = \frac{e^{2x} - 2xe^{2x}}{(e^{2x})^{2}}

y' = \frac{e^{2x}(1 - 2x)}{e^{4x}}

y' = \frac{1 - 2x}{e^{4x}}

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