Derivative of Exponential Function (Fully Explained!)

Do you want to learn an easy method for differentiating any exponential function?

Jenn (B.S., M.Ed.) of Calcworkshop® teaching how to find the derivative of an exponential function

Jenn, Founder Calcworkshop^®, 15+ Years Experience (Licensed & Certified Teacher)

I thought so.

What Is An Exponential Function

As you probably know, an exponential function is when the variable is the power rather than the base.

The base is always a positive integer greater than 1 and is written in the form:

Exponential Function Equation

Rules Of Exponents

Additionally, some vital exponent properties, listed below, allow us to simplify and solve exponential functions that are pivotal to our successful ability to simplify derivatives of exponential functions.

Properties Of Exponents

Likewise, I should remind you probably the most famous exponential function in calculus is the natural exponential function, e, in which e = 2.7182…, and is denoted by:

Natural Exponential Function

The Steps

So, now that we’ve reviewed the basics of exponents, it’s now time to turn our attention to differentiation.

How do you take a derivative of a function when the variable is in the exponent?

All we have to do is follow these three easy steps:

Rewrite
Multiply by the natural log of the base
Multiply by the derivative of the exponent

Derivative Of Exponential

In fact, this formula and method work for any exponential function!

Examples

Let’s find the derivative, using our new derivative rule, for the following exponential functions.

Taking The Derivative Of An Exponential Function

See, differentiating exponential functions is a snap — it’s as easy as 1-2-3! is derived from a

This video lesson will look at exponential properties and how to take a derivative of an exponential function, all while walking through several examples in detail.

Let’s jump right in.

Video Tutorial w/ Full Lesson & Detailed Examples (Video)

calcworkshop jenn teaching derivative exponential function

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