Applying Implicit Differentiation

A series of calculus lectures.

How to Do Implicit Differentiation?
Steps to doing implicit differentiation to find dy/dx:

1. Take the derivative of both sides, multiplying by dy/dx
   
2. Get dy/dx alone on one side

Examples:

1. Given the equation x² + y² = 100, find dy/dx. Calculate the slope at the point (6,8).
2. Given the equation x³ + 4xy + y² = 13, find dy/dx. Evaluate dy/dx at the point (1,2).
3. Find dy/dx by implicit differentiation. 5 - x² = sin(y²).

Use implicit differentiation to find the equation of the tangent line at a point
Learn how to use implicit differentiation to calculate the equation of the tangent to the curve at a specific point.
Use implicit differentiation to find the first derivative of y, or y', or y prime.
Plug the given point into the first derivative to get the slope of the tangent line, m.
Plug the slope and the given point into the point-slope formula for the equation of the line.
Simplify to get the equation of the tangent line to the curve at that point.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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