Find the derivative of e2x

We need to find the derivative of the function e2x

Solution

We can find the derivative of gib=ven function using the chain rule.

Chain rule states that , if f and g are functions, then the chain rule expresses the derivative of their composition.
d/dx [f(g(x))] = f'(g(x)) g'(x)

First we will need to use the Chain Rule

dy/ dx= dy/ du X du / dx

It can also be expressed as

d/dx [f(g(x))] = f'(g(x)) g'(x)

In general, if k is a constant and f(x) = ekx then f´(x) = kekx .

Hence

f(x) = e2x

we get

f´(x) = 2e2x .

Answer

The derivative of the function e2x is 2e2x

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