EXAMPLE 1
Find dx/dt:
xy = 4
To solve, you start with:
x • dy/dt + y • dx/dt = 0
EXAMPLE 2
Find dy/dt:
12x² = y³ - 24
In contrast to Example 1, you begin solving the problem with x • dx/dt:
24x • dx/dt = 3y² • dy/dt
As you can see, one solution begins with x • dy/dt and another solution begins with x • dx/dt.
Why?
COMPLETE WORKED PROBLEMS (FOR REFERENCE):
EXAMPLE 1:
Given:
xy=4
dy/dt=1
y=.5
Find dx/dt
Solution to Example 1:
x = 4/y = 4/.5 = 8
x • dy/dy + y • dx/dt
8•1 + .5 dy/dt = 0
dx/dt = 8/.5=16
EXAMPLE 2:
Given:
12x² = y³ - 24
dx/dt= -6
x= -.5
Find dy/dt
Solution to Example 2:
12•(-.5)² = y³ - 24
27=y³
y=3
24x • dx/dt = 3y² * dy/dt
24•(-.5)²•-6 = 3•(3)² •dy/dt
dy/dx = 72/27 = 8/3
Find dx/dt:
xy = 4
To solve, you start with:
x • dy/dt + y • dx/dt = 0
EXAMPLE 2
Find dy/dt:
12x² = y³ - 24
In contrast to Example 1, you begin solving the problem with x • dx/dt:
24x • dx/dt = 3y² • dy/dt
As you can see, one solution begins with x • dy/dt and another solution begins with x • dx/dt.
Why?
COMPLETE WORKED PROBLEMS (FOR REFERENCE):
EXAMPLE 1:
Given:
xy=4
dy/dt=1
y=.5
Find dx/dt
Solution to Example 1:
x = 4/y = 4/.5 = 8
x • dy/dy + y • dx/dt
8•1 + .5 dy/dt = 0
dx/dt = 8/.5=16
EXAMPLE 2:
Given:
12x² = y³ - 24
dx/dt= -6
x= -.5
Find dy/dt
Solution to Example 2:
12•(-.5)² = y³ - 24
27=y³
y=3
24x • dx/dt = 3y² * dy/dt
24•(-.5)²•-6 = 3•(3)² •dy/dt
dy/dx = 72/27 = 8/3