This document provides instructions and examples for taking derivatives of functions written implicitly and explicitly. It begins with examples of taking derivatives of explicitly defined functions written in terms of x and rewriting them in terms of y. Next, it discusses taking derivatives of implicitly defined functions, using the product rule and solving for the derivative of y, y'. Examples are worked through, such as finding that the derivative of xy = 5 is y' = -y/x. The document aims to teach how to take derivatives of various functions written in different forms.

1. Calculus Drill
Change each function to be
written in terms of y. Then
take the derivative.
 1. ƒ (x) = x2 +5x – 9
 2. ƒ(x) = x2√2x+1
 3. ƒ(x) = (2x2 + 3x)3

2. Find the derivative!
3 5
1. ƒ(x) = √x(√x + √x)

3. Find the derivative!
x
x + 1
3. ƒ(x) =
4

4. Find the Equation of the
tangent to the graph at
1
√x2+7
x = 3
3.ƒ(x) =

5. Calculus Objective
STW take
derivatives implicitly

6. Derivatives of Y
The derivative of y is
y’ or dy/dx.
Everything else you
do the same.

7. Examples
1. x + y = 10
Derivative 1 + y’ = 0
Solve for y’
y’ = –1

8. Examples
2. 2x2 + y2 = 5
Der. 4x + 2yy’ = 0
Solve for y’
y’ = – 2x/y

9. Examples
3. xy = 5
Derivative use the
product rule
u = x v= y
u’ = 1 v’ = y’

10. Examples
u = x v= y
u’ = 1 v’ = y’
Der. xy’ + y = 0
Solve for y’
 –y/x = y’