Aim 14 implicit differentiation.notebook
September 30, 2015
HW Solutions
5. P. 158
#1­29(odd), 39, 56 1. 3cos(3x+1)
39. a. ­6sin(6x+2) b. same
3. ­√3sin(√3x)
5. 2sinx (1+cos x)-2
56. a. 2/3
7. -sin2x cos x
b. 5+2
π
9. 3 sin(π/2-3t)
c. 15-8π
11. 4/π (cos 2t-sin5t)
d. 2/3+24
13. -2(x+√x)-3(1+(2√x)-1)
4
15. -5sin-6x cos x+3cos2x sinx
e. (1/3)(-3)=-1
17. 4 sin3x sec24x+3sin2x cos x tan(4x)
f. 1/3
19. -3(2x+1)-3/2
2√8
21. -6sin(3x-2)cos(3x-2)
g. -2(-4)-35
23. -42(1+cos2(7x))cos (7x)sin(7x)
h. 8/3-6
25. -sec2(2-x)
27. x cosx+sin x
√64+4
2√xsinx
29. 2sec2x tan x
Chain Rule
Sep 28­2:03 PM
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Aim 14 implicit differentiation.notebook
September 30, 2015
Sep 30­9:16 AM
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Aim 14 implicit differentiation.notebook
September 30, 2015
Sep 30­9:18 AM
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Aim 14 implicit differentiation.notebook
September 30, 2015
Aim 14: Implicit Differentiation
HW: P. 167 # 1­7(odd), 9, 13, 15, 17, 27, 49, 51 (Due Tuesday)
Find the slope of the line tangent to the circle at x=3
x2+y2=16
A given equation in x and y defines the function f implicitly if the graph of y=f
(x) coincides with a portion of the graph of the equation
May 24­1:03 PM
4
Aim 14 implicit differentiation.notebook
September 30, 2015
Aim 14: Implicit Differentiation
HW: P. 167 # 1­7(odd), 9, 13, 15, 17, 27, 49, 51
Folium of Descartes
x3+y3=3xy
May 24­1:10 PM
5
Aim 14 implicit differentiation.notebook
September 30, 2015
Aim 14: Implicit Differentiation
HW: P. 167 # 1­7(odd), 9, 13, 15, 17, 27, 49, 51
Find the derivative of xy=6
May 24­1:12 PM
6
Aim 14 implicit differentiation.notebook
September 30, 2015
Aim 14: Implicit Differentiation
HW: P. 167 # 1­7(odd), 9, 13, 15, 17, 27, 49, 51
Given the equation y2­x+1=0, find the slope of the line tangent to the graph at x=3
Oct 21­11:46 AM
7
Aim 14 implicit differentiation.notebook
September 30, 2015
Aim 14: Implicit Differentiation
HW: P. 167 # 1­7(odd), 9, 13, 15, 17, 27, 49, 51
Find the derivative of x3­y3=6xy
Oct 21­11:39 AM
8
Aim 14 implicit differentiation.notebook
September 30, 2015
Aim 14: Implicit Differentiation
HW: P. 167 # 1­7(odd), 9, 13, 15, 17, 27, 49, 51
Consider the equation y3+3x2y+13=0
a. Find dy/dx
b. Find the equation of the line(s) tangent to the graph at y=­1.
Oct 24­8:12 AM
9
Aim 14 implicit differentiation.notebook
September 30, 2015
Aim 14: Implicit Differentiation
HW: P. 167 # 1­7(odd), 9, 13, 15, 17, 27, 49, 51
Given the equation: x2+xy+y2=7
a. Show that dy/dx is equal to b. Find the equation(s) of the line(s) tangent to the graph at x=1.
c. At what point(s) is the tangent vertical?
Oct 25­11:45 AM
10
Aim 14 implicit differentiation.notebook
September 30, 2015
Aim 14: Implicit Differentiation
HW: P. 167 # 1­7(odd), 9, 13, 15, 17, 27, 49, 51
Find dy/dx given the equation:
sin(xy)+x=2
Sep 25­7:17 AM
11
Aim 14 implicit differentiation.notebook
September 30, 2015
Aim 14: Implicit Differentiation
HW: P. 167 # 1­7(odd), 9, 13, 15, 17, 27, 49, 51
Finding Second Derivatives
2
x2+y =25
a. find dy/dx b. find d2y/dx2
Sep 28­8:36 AM
12
Aim 14 implicit differentiation.notebook
September 30, 2015
Aim 14: Implicit Differentiation
HW: P. 167 # 1­7(odd), 9, 13, 15, 17, 27, 49, 51
If the derivative of an equation is dy/dx=2xy+y2, find the second derivative
Sep 28­8:37 AM
13
Aim 14 implicit differentiation.notebook
September 30, 2015
Sep 23­10:06 AM
14