Unit 3: Differentiation - Composite, Implicit, and Inverse Functions

Question 1

Implicit Differentiation

Answer 1

• Take the derivative of everything you see with respect to the independent variable. Do not forget the product, quotient, or chain rules! Don’t forget derivative of a constant is 0! (not be confused with 0! which is 1.)
• If you’re asked for the derivative at a point, plug in the point now and then solve for the derivative.
• If you’re asked for dy/dx, then solve for the derivative (which could be on both sides at this point, so it’s an Algebra I problem).

Question 2

Finding points on the curve with horizontal tangent line

Answer 2

1. find implicit differentiation of f(x)
2. set it equal to 0
3. have y=x equation and plug y into the ys in f(x)
4. solve for x and plug the value into the og f(x) to find y value

Question 3

Finding points on the curve with vertical tangent line

Answer 3

1. find implicit differentiation of f(x)
2. find where the equation equals undefined
3. plug it into all the ys in the og f(x) and find x value
4. plug the x value into the og f(x) again to find the y value.

Question 4

Derivatives of inverse trig functions

Answer 4

https://docs.google.com/document/d/1a4qXEdAkb_seNwiecrZDmu7rP5sQ0n2YJ3W4ewlVUkM/edit?usp=sharing

Question 5

Derivatives of a^x and a^u

Answer 5

https://docs.google.com/document/d/1a4qXEdAkb_seNwiecrZDmu7rP5sQ0n2YJ3W4ewlVUkM/edit?usp=sharing