Solving Implicit Differential Equations
Learning Objective
I can solve implicit differential equations using differentiation and algebra.
Key Concepts
Implicit differentiation is a technique used to find the derivative of functions where one variable is not explicitly expressed in terms of another.
When using implicit differentiation, we differentiate both sides of the equation with respect to a variable (typically x) and then solve for y prime, which represents dy/dx.
When differentiating terms involving 'y' with respect to 'x', it's important to apply the chain rule, treating 'y' as a function of 'x', which introduces a y prime term.
Practice Questions
This lesson includes 12 practice questions to reinforce learning.
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1. What is the primary difference between explicit and implicit differentiation?
2. When using implicit differentiation, why do we apply the chain rule when differentiating terms involving 'y' with respect to 'x'?
3. Given the equation x² + y² = 25, find dy/dx using implicit differentiation.
...and 9 more questions
Educational Video
Implicit Differentiation
Professor Dave Explains