Differentiation & Integration

Question 1

What is the Chain rule?

When is it used?

Find U and/or V for y = (3x^4+x)^5

Answer 1

• Used to differentiate a composite function (function inside a function)

– > dy/dx =dy/du x du/dx

– > y = (3x^4+x)^5 where 3x^4+x is u

Question 2

What is the Product rule?

When is it used?

Find U and/or V for y = x^2 sin(x)

Answer 2

• Used when adding functions

dy/dx = U dv/dx + V du/dx

y = x^2 sin(x) where U = x^2 and V = sin(x)

Question 3

What is the Quotient rule?

When is it used?

Find U and/or V for y = x / (2x + 5)

Answer 3

• Used when dividing functions

dy/dx = ( V dy/dx - U du/dx ) / v^2

U = x

V = 2x + 5

Question 4

How do you find the maximum of a graph?

How do you determine if it is a maximum or minimum?

Answer 4

• Find dy/dx and set = to 0

Sub in x co-ordinate and is
(-) then maximum
(+) then minimum