# Lesson Worksheet: Implicit Differentiation Mathematics • Higher Education

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

Q1:

Given that , find .

• A
• B
• C
• D0

Q2:

Find the slope of the tangent to the curve at .

• A
• B
• C
• D

Q3:

Find the equation of the tangent to that has slope .

• A
• B
• C
• D

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:

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

• A
• B
• C
• D

Q7:

Given that , determine by implicit differentiation.

• A
• B
• C
• D
• E

Q8:

Consider the equation .

Using implicit differentiation, find an expression for in terms of and .

• A
• B
• C
• D

For the semicircle where , express explicitly in terms of ; then, differentiate this expression to get an expression for in terms of .

• A
• B
• C
• D

Q9:

The equation describes a curve in the plane.

Find the coordinates of two points on this curve, where .

• A and
• BThe curve does not pass through the point .
• C and
• D and
• E and

Determine the equation of the tangent at the points where and the -coordinate is positive.

• A
• B
• C
• D
• E

Find the coordinates of another point, if it exists, at which the tangent meets the curve.

• AThey do not meet at any other point.
• B
• C
• D
• E

Q10:

Find , given that .

• A
• B
• C
• D

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