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## Calculus, all content (2017 edition)

### Course: Calculus, all content (2017 edition)>Unit 2

Lesson 27: Exponential functions differentiation

# Differentiating exponential functions review

Review your exponential function differentiation skills and use them to solve problems.

## How do I differentiate exponential functions?

First, you should know the derivatives for the basic exponential functions:
start fraction, d, divided by, d, x, end fraction, left parenthesis, e, start superscript, x, end superscript, right parenthesis, equals, e, start superscript, x, end superscript
start fraction, d, divided by, d, x, end fraction, left parenthesis, a, start superscript, x, end superscript, right parenthesis, equals, natural log, left parenthesis, a, right parenthesis, dot, a, start superscript, x, end superscript
Notice that e, start superscript, x, end superscript is a specific case of the general form a, start superscript, x, end superscript where a, equals, e. Since natural log, left parenthesis, e, right parenthesis, equals, 1 we obtain the same result.
You can actually use the derivative of e, start superscript, x, end superscript (along with the chain rule) to obtain the general derivative of a, start superscript, x, end superscript.

## Practice set 1: exponent is $x$x

Problem 1.1
• Current
f, left parenthesis, x, right parenthesis, equals, minus, 4, e, start superscript, x, end superscript
f, prime, left parenthesis, x, right parenthesis, equals, question mark

Want to try more problems like this? Check out this exercise.

## Practice set 2: exponent is a polynomial

Problem 2.1
• Current
y, equals, e, start superscript, left parenthesis, 3, x, squared, minus, 4, right parenthesis, end superscript
start fraction, d, y, divided by, d, x, end fraction, equals, question mark