Examples on Derivative of e2x
Some examples related to derivative of e2x are,
Example 1: Find derivative of e8x.
Solution:
Let y = e8x
⇒ y’ = (d/dx) e8x
Applying chain rule
y’ = (d/d 8x) (e8x).(d/dx) (8x)
⇒ y’ = (e8x).8
⇒ y’ = 8e8x
Example 2: Evaluate derivative f(x) = (x3 + 5x2 + 2x + 7)e2x
Solution:
f(x) = (x3 + 5x2 + 2x + 7).e2x
⇒ f'(x) = (d /dx)[(x3 + 5x2 + 2x + 7)e2x]
Applying Product Rule
f'(x) = (d /dx)[(x3 + 5x2 + 2x + 7)].e2x + (x3 + 5x2 + 2x + 7).(d /dx)[e2x]
⇒ f'(x) = (3x2 + 10x +2).e2x + (x3 + 5x2 + 2x + 7)(2e2x)
⇒ f'(x) = (3x2 + 10x +2)e2x + 2.(x3 + 5x2 + 2x + 7)e2x
Example 3: Evaluate derivative e5x+ x.e2x
Solution:
Let z = e5x + x.e2x
Differentiating
z’ = (d/dx) [e5x + x.e2x]
⇒ z’ = (d/dx) e5x + (d/dx)[x.e2x]
Applying Chain Rule and Product Rule
z’ = 5.e5x + (d/dx)(x).e2x + x.(d/dx)(e2x)
⇒ z’ = 5.e5x + e2x + x.(2e2x)
Example 4: Find derivative of e-x.
Solution:
= (d /dx) [e-x]
= -e-x
Example 5: Find derivative of e2xcos x
Solution:
Applying Product Rule
= (d/dx) [e2x cos x]
= e2x d/dx (cos x) + cos x d/dx (e2x)
= e2x (-sin x) + cos x.(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