Implicit Differentiation Practice Problems
These problems follow the implicit differentiation lesson. They start with circles and simple curves and build up to products, trig and exponential terms, and a second derivative.
The method
- Differentiate both sides with respect to
. - Multiply the derivative of every
-term by : . - Collect the
terms on one side. - Factor out
and divide.
Common mistakes to watch for
- Forgetting
when differentiating a -term. - Skipping the product rule on terms like
and . - Leaving the constant side as a constant: it differentiates to 0.
- Dividing before collecting all the
terms.