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 .