# Implicit differentiation modules

## Overview

After completing this section, students should be able to do the following.

- Implicitly differentiate expression.
- Find the equation of the tangent line for curves that are not plots of functions.
- Understand how changing the variable changes how we take the derivative.
- Understand the derivatives of functions that are not defined explicitly in terms of an independent variable .
- Explain the formula for the derivative of the natural log function.
- Calculate derivatives of logs in any base.
- Calculate the derivative of an exponential function, axax, where a>0a>0.

# Standard form

## Ximera Module

Two young mathematicians discuss the standard form of a line.

# Implicit differentiation

## Ximera Module

In this section we differentiate equations that contain more than one variable on one side.

# Derivatives of inverse exponential functions

## Ximera Module

We derive the derivatives of inverse exponential functions using implicit differentiation.

# Derivatives of inverse trigonometric functions

## Ximera Module

We derive the derivatives of inverse trigonometric functions using implicit differentiation.

# The Inverse Function Theorem

## Ximera Module

We see the theoretical underpinning of finding the derivative of an inverse function at a point.