Solving Implicit Differential Equations
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Objective
I can solve implicit differential equations using differentiation and algebra.
Part 1 of 4
Warm-up video
Professor Dave Explains · 11:45Vetted channel
We don't generate video — this one is by Professor Dave Explains on YouTube. The practice questions and exit ticket below were drafted by AI for this objective, and every question is editable in the teacher guide.
Part 2 of 4
Key concepts
3 concepts
- 1
Implicit differentiation is a technique used to find the derivative of functions where one variable is not explicitly expressed in terms of another.
- 2
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.
- 3
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.
Part 3 of 4
Practice
12 questions
What is the primary difference between explicit and implicit differentiation?
When using implicit differentiation, why do we apply the chain rule when differentiating terms involving 'y' with respect to 'x'?
Part 4 of 4
Exit ticket
Quick comprehension check
“Find dy/dx for the equation x³ + y³ = 6xy. Show all steps.”
Sample answer included in the free materials
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