7: Limits and Derivatives

Question 1

What is the constant rule?

Answer 1

If f(x) = c, where c is any real number, then f’(x) = 0

The derivative of any constant is 0. The graph of the constant function f(x) = c is a horizontal line which has a gradient of 0.

Question 2

How do you read dy/dx?

Answer 2

• dy/dx is read as the ‘derivative of y with respect to x’.
• Recall that the slope is change in y/change in x.

Question 3

What is the constant multiple rule?

Answer 3

If y = cf (x), where c is any real number, then y’ = cf’ (x)

The derivative of a constant time a function is the constant times the derivative of the function.

Question 4

What is the sum or difference rule?

Answer 4

If f(x) = u(x) +/- v(x) then f’(x) = u’ (x) +/- v’ (x)

The derivative of a function that is the sum or difference of two or more terms is the sum or difference of the derivative of the terms.