You forgot to take the derivative of e^(2x)CrossFit415 said:f(x)= xe^(2x)
(f • g)' = x • e(^2x) + e^(2x) • 1
The derivative of e^fx is e^fx multiplied by the derivative of fx, which is 2xe^(2x).
To solve for the derivative of e^fx, you can use the chain rule. First, take the derivative of the exponent, which in this case is 2x. Then, multiply it by the original function e^fx. This will give you 2xe^(2x) as the final answer.
No, the derivative of e^fx cannot be simplified any further. The answer of 2xe^(2x) is the most simplified form.
Sure, let's say we have the function f(x) = e^(2x). Using the chain rule, the derivative would be f'(x) = e^(2x) * (2x)' = 2xe^(2x).
Knowing the derivative of e^fx is important because it allows us to find the rate of change of a function at any given point. This can be useful in many areas of science and mathematics, such as in optimization problems and in determining the slope of a curve.