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.

Paper 1 Paper 2 Paper 3

Each paper is built from this unit’s 38 terms and is the same for everyone, so a teacher can assign “Unit 3, Paper 1” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.

Suggested time 36 min 33 points0/17 attempted

Inverse trig chain rule

Derivative of an inverse function

Derivative of arctan

Derivatives of inverse trig functions

Implicit differentiation is the chain rule on y

Inverse derivative formula

Chain rule with a table

Sign of an implicit second derivative

Second derivative implicitly

Higher-order derivatives of sine

Derivative of a variable base and exponent

Work outside in

Short answer 1. Define or explain: Implicit differentiation

3 pts

Short answer 2. Define or explain: Related rates as implicit differentiation

3 pts

Short answer 3. Define or explain: Derivative of a variable base with a variable exponent

3 pts

Short answer 4. Define or explain: The lost inner factor

3 pts

Free response

9 pts

Consider 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.