# 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:

Do the curves and intersect orthogonally at the origin?

• Ayes
• Bno

Q6:

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

• A
• B
• C
• D

Q7:

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

• A
• B
• C
• D

Q8:

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

Q9:

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

• A
• B
• C
• D

Q10:

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

• A
• B
• C
• D

Q11:

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

• A
• B
• C ,
• D ,

Q12:

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

• A ,
• B ,
• C ,
• D ,

Q13:

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

• A
• B
• C
• D

Q14:

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

• A
• B
• C
• D

Q15:

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

Q16:

A tangent to forms an isosceles triangle when taken with the positive - and -axes. What is the equation of this tangent?

• A
• B
• C
• D

Q17:

Given that , determine by implicit differentiation.

• A
• B
• C
• D
• E

Q18:

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 ,

Q19:

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

• A
• B
• C
• D

Q20:

The point lies on the curve . Find and the equation of the tangent to the curve at this point.

• A , equation of the tangent:
• B , equation of the tangent:
• C , equation of the tangent:
• D , equation of the tangent:

Q21:

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

• A
• B
• C
• D
• E

Q22:

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

• A
• B
• C
• D

Q23:

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

• A
• B
• C
• D

Q24:

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

• A
• B
• C
• D

Q25:

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

• A ,
• B ,
• C ,
• D ,