Composite & Implicit Differentiation unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Related rates as implicit differentiation
Vertical and horizontal tangents implicitly
The xy term needs the product rule
The lost inner factor
Derivative of a variable base with a variable exponent
Why dy/dx involves y
Sign of an implicit second derivative
Derivative of a variable base and exponent
Vertical tangent from an implicit derivative
Higher-order derivatives of sine
Where to evaluate an inverse derivative
Circle slope formula
Short answer 1. Define or explain: Implicit differentiation
3 ptsShort answer 2. Define or explain: Collect and factor
3 ptsShort answer 3. Define or explain: Derivative of an inverse function
3 ptsShort answer 4. Define or explain: Implicit second derivative sign
3 ptsFree response
9 ptsConsider the curve defined implicitly by x² + 2xy − y² = 7.
Show that the point (2, 1) lies on the curve, and find dy/dx in terms of x and y.
Write the equation of the line tangent to the curve at (2, 1).
Find the coordinates of all points on the curve at which the tangent line is vertical, and justify that the tangent is vertical rather than undefined for some other reason.