Implicit Differentiation
Find dy/dx for x2+y=x
dy/dx = 1-2x
Assume 2x+3y=12 and dy/dt = -2. Find dx/dt.
3
Write the equation of the tangent line to
f(x)=x3-2x+3 at x = 2.
y - 7 = 10(x - 2)
or
y = 7 + 10(x - 2)
Find dy. y = x2
dy = 2xdx
Find f'(x)
f(x) = x2 + √x + 1/x
f'(x) = 2x + 1/2x-1/2 - x-2
Find dy/dx when x = 2. y = x2
4
If x = y3 - y and dy/dt = 5. Find dx/dt when y = 2
55
Find the equation of the tangent line to
f(x) = 2x2 + 3x - 3 at x = 1
y - 2 = 7(x - 1)
or
y = 2 + 7(x - 1)
Find dV. V = 4/3πr3
dV = 4πr2dr
Find f'(x).
f(x) = 3xsin(x)
f'(x) = 3xcos(x) + 3sin(x)
Find dy/dx. 2xy + y2 = x + y
(1-2y)/(2x+2y-1)
A cube's surface area increases at a rate of 72 in2/sec. At what rate is the cube's edge changing when the edge length is 3 in?
2 in/sec
Approximate the value of f(.9) when
f(x) = 2x2 + 3x - 3
1.3
Find the change in y when y = x2 + 2x when x changes from 1 to 1.1
.4
Find f'(x)
f(x) = ex/2x
f'(x) = (2xex - 2ex)/4x2
Find dy/dx when x = 3. x2 + y2 = 25
-3/4
A spherical balloon is being inflated with the radius increasing at a rate of 2 cm/sec. At what rate is the volume changing when the radius is 1 cm?
8π cm3/sec or 25.1 cm3/sec
Approximate 2.992
8.94
Approximate the value of 2.992
8.94
Find f'(x).
f(x) = sin2(x)
f'(x) = 2sin(x)cos(x)
Find dy/dx at (-1, 0). 6x2+3xy+2y2+17y-6=0
6/7
A 13-foot ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house, the base is moving at the rate of 5 ft/sec. How fast is the top of the ladder sliding down the wall then?
-12 ft/sec
Approximate the value of √4.2
2.05
The radius of a spherical balloon is measured as 50 cm with a possible error of .2 cm. What is the maximum error in volume using those calculations?
2000π cm3
or
6283.2 cm3
Find f'(x)
f(x) = sin(x2)ln(3x+2)
3sin(x2)/(3x+2) + 2xcos(x2)ln(3x+2)