Calculus worksheet chapter 4 on derivatives:
- Find the derivative:
Use product rule
or multiply and then take the derivative.
- Find the derivative:
Use the chain rule. Let u = x+1 and y = u^3
- Find f’(x)
- You can do this derivative in 3 ways. Take the derivative of each piece, by quotient rule or by chain rule. Or combine this into one fraction and then use the quotient rule.
- Use the quotient rule:
- Find the derivative of
- Find the derivative of the following:
- Find the derivative:
- Find the derivative:
- Find the derivative:
- Find dy/dx given:
. Use
implicit differentiation:
32x +50y dy/dx = 0
50y dy/dx = - 32 x
dy/dx = -32x/50y
dy/dx = -16x/25y
- Find the derivative of y = sin(2x). Use the chain rule.
Let u = 2x.
du/dx = 2
y = sin u
dy/du = cos u = cos(2x)
dy/dx = dy/du * du/dx
dy/dx =2cos(2x)
- Find the derivative of
- Find the derivative of
- Find the derivative of
:
Use the chain rule:
- Find the derivative of
Use the chain rule twice. Let u = tan(5x).
du/dx = use chain rule let v = 5x
dv/dx = 5
u = tan v
du/dv = (secv)^2
du/dx = du/dv*dv/dx
- Find the derivative of
. Use the
chain rule.
- Find the derivative of
Use the Chain rule:
- Find the derivative
of:
Use two chain rules:
1. A conical tank has a radius of 160 cm and a height of 800 cm. Water is running out a small hole at the bottom. When the height of the tank is 600 cm, what is the rate of change of its volume V with respect to the height, h?
First note that the ratio of the height to the radius create a similar triangles: h/r=800/160 or r = h/r. So when the height is 600 cm, the radius is 120 cm.
2.