Product Rule
This rule states that if f(x) = g (x)h(x), then
f′(x)=g′(x)h(x) + g(x)h′(x).
Name this differentiation rule.
What is the Product Rule?
When differentiating y with respect to x, you must multiply by ______.
what is dy/dx?
If position is s(t)= 4t^(2), find velocity.
what is v(t) = 8t?
This is the formula for the volume of a sphere with radius r.
What is V = (4/3)pir^(3)
This is the formula for the area of a circle with radius r.
What is A = pi(r^2)
Differentiate:
f(x) = x cos(x)
what is cos(x) - x sin(x)?
Find dy/dx if x+y =10
what is -1?
If velocity is v(t) = 6t−3, find acceleration.
What is a(t) = 6?
Radius increasing at dr/dt = 3cm/min, r = 5
what is 300pi cubic centimeters per minute?
This is the formula for the volume of a cube with side length s.
What is V = s^3?
Differentiate:
f(x) = x^(3) ln(x)
what is 3x^(2)ln(x) + x^(2)?
Find dy/dx if x^(2)+y = 7
what is -2x?
A ball’s position along a straight track is
s(t)=2t^(2)
Find the rate at which the ball’s position is changing.
Choices:
A) Position
B) Velocity
C) Acceleration
What is velocity?
Given dV/dt = 20, r = 4
What is 5/(16pi) centimeters per second?
The side length of a cube is increasing at 3 centimeters per second. This is the rate at which the volume is increasing when the side length is 2 centimeters.
What is 36 cubic centimeters per second?
Differentiate:
f(x) = (2x-1)e^(x)
what is 2e^(x) + (2x+1)e^(x)?
Find dy/dt for 3x + 4y =12, when dx/dt = 1
what is dy/dt = -3/4?
Velocity is the ______ of the position function.
What is the derivative?
Given dr/dt = -0.5, r = 10
What is -200pi cubic centimeters per min?
The area of a circle is increasing at 10pi square centimeters per second.
This is the rate at which the radius is increasing when the radius is 5 centimeters.
What is 1 centimeter per second?
Differentiate:
f(x) = x^(2)tan(x)
what is 2xtan(x) + x^(2)sec^(2)(x) ?
Find the slope of the curve
x^(2)+y^(2)=25
at the point (3,4) and let dx/dt = 1.
what is -3/4?
Position tells us ______.
What is where the object is located?
The radius of a spherical metal ball is increasing at 0.2 centimeters per second. This is the rate at which the surface area is increasing when the radius is 8 centimeters.
What is 12.8pi square centimeters per second?
The volume of a cube is increasing at 96 cubic centimeters per second.
When the side length is 4 centimeters, this is the rate at which the side length is increasing.
What is 2 centimeters per second?