# Derivative of Exponential

Taught by TheMathDude
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Lesson Summary:

In this lesson, you will learn the derivative rule for exponential functions, specifically e to the x. The rate of change for the exponential function is just the exponential function, making it a useful property for solving differential equations. By using chain rule, you can easily find the derivative for more complicated functions, and combining them with product rule can make finding the derivative even simpler. Remember that if you have a function that's just e raised to some growth rate constant, you can find the rate of change by just taking the original function and multiplying back by the growth rate constant.

Lesson Description:

Know and be able to apply the derivative rule for exponential functions.

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• How do you take the derivative of an exponential function?
• Why is the derivative of e^x still e^x?
• Why is it a big deal when the derivative of a function is itself?
• What is the derivative of b^x?
• How does the chain rule work for exponential functions?
• What is the derivative of e^(nx)?
• What is a quick and easy way to find the derivative of e^x at a point?
• What is the derivative of e^(2x^2 + 2)?
• How do you find the derivative of e^(2x^2 + 2)^2?
• What is the derivative of x*e^(0.1x)?
• #### Staff Review

• Currently 4.0/5 Stars.
This lesson explains the concept of taking the derivative of e^x, which is one of the simplest derivatives to take, and it is also one of the most interesting derivatives. This is a great introduction to taking derivatives of the exponential function and why it works the way it does. Many different examples are shown, solved, and explained in this lesson.