Implicit differentiation modules
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.
Two young mathematicians discuss the standard form of a line.
In this section we differentiate equations that contain more than one variable on one side.
Derivatives of inverse exponential functions
We derive the derivatives of inverse exponential functions using implicit differentiation.
Derivatives of inverse trigonometric functions
We derive the derivatives of inverse trigonometric functions using implicit differentiation.
The Inverse Function Theorem
We see the theoretical underpinning of finding the derivative of an inverse function at a point.