Lesson 7 of 18Article16 min
Implicit Differentiation & Higher Derivatives
Circles and many relations are given as F(x,y) = 0. Differentiate both sides treating y as y(x), using the chain rule on every y term.
When y is not solved for x
Circles and many relations are given as F(x,y) = 0. Differentiate both sides treating y as y(x), using the chain rule on every y term.
After finding y′, you can differentiate again to get y″ in terms of x and y — useful for concavity on implicit curves.
Higher-order derivatives
- f″ = (f′)′ — acceleration if f′ is velocity.
- Notation: f″(x), d²y/dx², y″.
- Taylor polynomials later use f, f′, f″, f‴ at a point.