Differentiation 1

Question 1

What are the different ways of denoting differentiation?

Answer 1

• dy/dx
• y’
• f’(x)

Question 2

What is differentiation?

Answer 2

• the gradient function tells you the gradient at any point
• it measures the rate of change of y with respect to x

Question 3

How do you differentiate from first principles?

Answer 3

Question 4

How do you find the gradient at any point?

Answer 4

• substitute what x= into the gradient function

Question 5

How do you find stationary points?

Answer 5

• 1st derivative tells you where the stationary point(s) is/are
• put dy/dx = 0 to find the values of x
• then substitute x into the original equation to find the y coordinates
• 2nd derivative tells you the type of stationary point(s)
• if positive: it is a minimum
• if negative: it is a maximum