2015 Calc Lesson 17 Implicit Differentiation.notebook
November 28, 2016
11/28/15
Exam 1 Thursday
AIM: What is Implicit Differentiation?
Warm­up:
Find dy for each of the following:
dx
2) xy=5
1) y = 3x+5
Oct 8­12:01 PM
For these, y is a function explicitly defined in terms of x.
For these, y is a function implicitly defined in terms of x.
xy=12
y=x+1
x+xy+y= 5
y=sin x
y=cos xy
Be able to explain what makes a function implicitly defined vs. explicitly defined.
Jul 23­1:39 PM
1
2015 Calc Lesson 17 Implicit Differentiation.notebook
November 28, 2016
= "Derivative of y with respect to x"
Nov 21­2:05 PM
Implicit Differentiation
ex. ex. ex. 2
2y
Aug 25 ­ 12:56 PM
2
2015 Calc Lesson 17 Implicit Differentiation.notebook
November 28, 2016
Implicit Differentiation
Take the derivative of each term with respect to x and solve for dy/dx.
ex. Find dy/dx for 2y
+3=2x
2y =2x­3
=
Aug 25 ­ 1:07 PM
ex. Find dy/dx for sinx+cosy=2y ex. Find dy/dx for Aug 25 ­ 1:08 PM
3
2015 Calc Lesson 17 Implicit Differentiation.notebook
November 28, 2016
ex. a. Show that Aug 25 ­ 1:11 PM
4