Implicit Differentiation
2x-y=-3; find dy/dx
2
4x2-y2=9 ; find dy/dx
4x/y
x2+y2=2xy ; find dy/dx
a) x/1-y b) y+x/y-x c) 1 d) -x/y
c
y4+3y-4x3=5x+1 ; find dy/dx
12x2+5/4y3+3
5x2-3xy+y=2 ; find dy/dx, then evaluate at (0,2)
a) -2 b) -5/4 c) 0 d) 6
d
xey=y3+4x+1 ; find dy/dx
a) 4-ey/xey-3y2 b) 3y2+4-ey/xey
c) 5-ey/xey-3y2 d) 4-ey/ey-3y2
a
xy=sin(y)+x2y2 ; find dy/dx
2xy2-y/x-cos(y)-2x2y
x=sin(xy) ; find dy/dx
1/xcos(xy) - y/x
A 50ft ladder is placed against a building. The base of the ladder is resting on an oil spill, and it slips at a rate of 3 ft/min. Find the rate of change of the height of the top of the ladder above the ground at the instant when the base of the ladder is 30ft from the buildings base.
-2.25 ft/sec
A spherical balloon is being inflated so that its diameter is increasing at a rate of 2 cm/min. How quickly is the volume of the balloon increasing when the diameter is 10cm?
dV/dt=100pi cm3/min
A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 4 ft/sec. After 12 seconds, how rapidly is the area enclosed by the ripple increasing.
dA/dt=384pi ft2/sec
The radius of a cylinder is increasing at a rate of 1 m/hr, and the height of the cylinder is decreasing at a rate of 4 m/hr. At a certain instant, the base radius is 5m, and the height is 8m. What is the rate of change of the volume of the cylinder at that instant?
dV/dt=-20pi m3/hr
A funnel in the shape of an inverted cone is 30cm deep and has a diameter across the top of 20cm. Liquid is flowing out of the funnel at a rate of 12 cm3/sec. At what rate is the height of the liquid decreasing at the instant when the liquid in the funnel is 20cm deep.
dh/dt=-27/100pi cm/sec