From the course: Complete Guide to Calculus Foundations for Data Science
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Exponential derivatives
From the course: Complete Guide to Calculus Foundations for Data Science
Exponential derivatives
- [Instructor] Next, let's take a look at exponential derivatives. These are derivatives that contain exponents where the variable itself is in the exponent, such as e to the x. This video will not cover functions such as x squared since you could use the power rule to solve those types of functions. Let's begin by looking at general exponential functions in the format of f of x equals a to the x, where a is a real number greater than zero, like I mentioned previously, you cannot use the power rule to solve this function because the variable is in the exponent itself instead of the base. If you wish to get the derivative of a function f of x equals a to the x, then you'll derive it in the following format, so you'll have f prime of x equals the natural log of a multiplied by a to the x. Essentially, this will simplify your function when it's derived to a constant natural logarithmic value multiplied by your original exponential function. Let's look at an example where f of x equals…
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