Derivative of e2x by Logarithmic Differentiation
Logarithmic differentiation is used to differentiate exponential function and is thus used to find the derivative of e2x.
let, y = e2x
ln y = ln e2x
ln y = 2x ln e (ln e = 1)
ln y = 2x
Differentiating both sides with respect to x,
(1/y) (dy/dx) = 2(1)
dy/dx = 2y
Substituting y = e2x
d/dx(e2x) = 2e2x
Derivative of e^2x
Derivative of e2x is 2e2x. Derivative of e2x refers to the process of finding the change in the exponential function e2x with respect to the independent variable x. e2x is an exponential functions that are power functions with the base of Euler’s Number.
In this article, we will learn in detail about the derivative of e to the power 2x, its formula, proof and examples based on it.
In this article, we will learn about the derivative of e2x and its formula including the proof of the formula using the first principle of derivatives, product rule, and chain rule in detail.
Table of Content
- What is Derivative in Math?
- What is Derivative of e2x?
- Proof of Derivative of e2x
- Derivative of e2x by Logarithmic Differentiation
- nth Derivative of e2x