Students will be able to
- use the chain rule in order to implicitly differentiate functions,
- know when it is simpler to use implicit differentiation even though it is possible to rearrange the relation and use explicit differentiation,
- find the slope of a curve at a given point using implicit differentiation,
- find the equation of a tangent to a curve at a given point using implicit differentiation,
- find higher-order derivatives of a function using implicit differentiation.
Students should already be familiar with
- differentiating polynomial, trigonometric, and rational functions,
- the chain, product, and quotient rules of differentiation,
- higher-order derivatives,
- equations of tangents and normals to a curve.
Students will not cover
- differentiating exponential and logarithmic functions.