Applying Implicit Differentiation
A series of calculus lectures.
How to Do Implicit Differentiation?
Steps to doing implicit differentiation to find dy/dx:
- Take the derivative of both sides, multiplying by dy/dx
- Get dy/dx alone on one side
Examples:
- Given the equation x2 + y2 = 100, find dy/dx. Calculate the slope at the point (6,8).
- Given the equation x3 + 4xy + y2 = 13, find dy/dx. Evaluate dy/dx at the point (1,2).
- 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.
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