Worksheet: An Introduction to the Definition of the Derivative

Practice applying the formal definition of the derivative. In this worksheet, calculate the derivative of polynomial functions using the definition of a derivative in terms of a limit.

Q1:

If the function , find .

Q2:

If the function , find .

Q3:

If the function , find .

Q4:

If the function , find .

Q5:

Let . Use the definition of derivative to determine . What is the gradient of the tangent to its graph at ?

A, the gradient of the tangent at point
B, the gradient of the tangent at point
C, the gradient of the tangent at point
D, the gradient of the tangent at point
E, the gradient of the tangent at point

Q6:

Let . Use the definition of derivative to determine . What is the gradient of the tangent to its graph at ?

A, the gradient of the tangent at point
B, the gradient of the tangent at point
C, the gradient of the tangent at point
D, the gradient of the tangent at point
E, the gradient of the tangent at point

Q7:

Let . Use the definition of derivative to determine . What is the gradient of the tangent to its graph at ?

A, the gradient of the tangent at point
B, the gradient of the tangent at point
C, the gradient of the tangent at point
D, the gradient of the tangent at point

Q8:

Let . Use the definition of derivative to determine . What is the gradient of the tangent to its graph at ?

A, the gradient of the tangent at point
B, the gradient of the tangent at point
C, the gradient of the tangent at point
D, the gradient of the tangent at point

Q9:

Find the derivative of the function using the definition of derivative, and then state the domain of the function and the domain of its derivative.

A, ,
B, ,
C, ,
D, ,
E, ,

Q10:

Find the derivative of the function using the definition of derivative, and then state the domain of the function and the domain of its derivative.

A, ,
B, ,
C, ,
D, ,
E, ,

Q11:

Find the derivative of the function using the definition of derivative, and then state the domain of the function and the domain of its derivative.

A, ,
B, ,
C, ,
D, ,
E, ,

Q12:

Let . Use the definition of derivative to determine . What is the gradient of the tangent to its graph at ?

A, the gradient of the tangent at point
B, the gradient of the tangent at point
C, the gradient of the tangent at point
D, the gradient of the tangent at point

Q13:

Let . Use the definition of the derivative to determine .

Q14:

Determine the derivative of the function using the definition of the derivative.

Q15:

Evaluate .

Q16:

Evaluate .