Derivatives
udv+vdu
The Product Rule
Derivative of sinx
cosx
What is the limit as x approaches 0 from the negative side lxl/x
-1
What is the implicit differentiation of d/dx (sin y)
(cos y) ⋅ dx/dx
True or False:
Related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known.
True
Formula for the Quotient Rule
udv-vdu/v2
Derivative of cotx
cosec2x
What does x->1 mean?
As you approach 1 on the x-axis or as x approaches 1 on the x-axis
What is the implicit differentiation of y2 + x2 = 9
dy/dx = -x/y
The rate of change is usually with respect to...
Time
Formula for the Chain Rule
f(g(x)) = f'(g(x))⋅g'(x)
Derivative of secx
secx ⋅ tanx
What is the limit as x approaches 0 1/x
∞
What differentiation rule is d/dx k = 0
Constant Rule
Air is being pumped into a spherical balloon at a rate of 6 ft3/min. Find the rate of change of the radius when the radius is 2 ft.
Hint. Use V = 4/3 𝝅r3
3/8𝝅 ft/min or 0.119 ft/min
Find dy/dx given
y= (8-2x)3
y'= -6(8-2x)2
What is the trig value of sin 30°
1/2
What is the limit as x approaches ∞ 1/x
0
Power Rule
Given x and y are both differentiable functions of t and y = 3x2, find dy/dt when x = 2 given dx/dt = 4 when x = 2
48
Find dy/dx given
x2 + y2 = 169
-x/y
What is the trig value of tan 45°
1
What is the limit as x approaches 0 cosx
1
What is the Log differentiation of d/dx ln(x)
1/x
A ladder 10 ft long rests against a vertical wall. I f the bottom of the ladder slides away from the wall at a rate pf 1 foot per second, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall?
-3/4 ft/sec