# Worksheet: Implicit Differentiation

In this worksheet, we will practice using implicit differentiation to differentiate functions defined implicitly.

Q1:

Find the equation of the tangent to that has slope .

• A
• B
• C
• D

Q2:

Find the equation of the tangent to the curve at the point .

• A
• B
• C
• D
• E

Q3:

Given that , find .

• A
• B
• C
• D2

Q4:

Given that , determine by implicit differentiation.

• A
• B
• C
• D
• E

Q5:

Find the slope of the tangent to the curve at the point .

• A
• B
• C
• D

Q6:

At a point on the curve with , , the tangent makes an angle of with the positive -axis. Find the equation of the tangent at that point.

• A
• B
• C
• D

Q7:

Find the equation of the tangent to the curve at the point .

• A
• B
• C
• D

Q8:

Find the points on the curve at which the tangent is parallel to the axis.

• A
• B
• C,
• D,

Q9:

Find the points that lie on the curve at which the tangent is parallel to line .

• A,
• B,
• C,
• D,

Q10:

Find the equation of the tangent to the curve at the point .

• A
• B
• C
• D

Q11:

The tangent at to the curve makes a positive angle with the positive -axis. Find this angle.

Q12:

Given that , determine by implicit differentiation.

• A
• B
• C
• D
• E

Q13:

Find the equations of the two tangents to the circle that are inclined to the positive -axis by an angle whose tangent is 2.

• A,
• B,
• C,
• D,

Q14:

Find the equation of the tangent to the curve at the point .

• A
• B
• C
• D

Q15:

The tangent at to the curve makes a positive angle with the positive -axis. Find this angle.

Q16:

Find the equation of the tangent to the curve at the point .

• A
• B
• C
• D

Q17:

Determine the points on a curve at which the tangent to the curve is perpendicular to the straight line .

• A
• B
• C
• D

Q18:

Find the equations of the normals to the curve at the points on the -axis.

• A,
• B,
• C,
• D,

Q19:

Find the equation of the tangent to the curve at the point .

• A
• B
• C
• D

Q20:

Given that , find .

• A
• B
• C16
• D

Q21:

If , find the value of at .

Q22:

Find, for , the tangent to that has slope , giving your equation in terms of .

• A
• B
• C
• D

Q23:

Find the equation of the tangent to that passes through .

• A
• B
• C
• D

Q24:

A tangent to has slope . What is the equation of this line?

• A
• B
• C
• D

Q25:

Find , given that .

• A
• B
• C
• D