IXL - Find derivatives using implicit differentiation (Calculus practice)

Find the derivative of

with respect to

–

Write your answer as a rational expression in one or both variables

(

and

′

ref_doc_title.

Learn with an example

question

Find the derivative of

with respect to

Write your answer as a rational expression in one or both variables

(

and

′

key idea

A function

of a variable

may be given in one of two ways: explicitly or

implicitly.

An explicit function

of a variable

is defined by an equation of the form

(

)

An implicit function

of a variable

satisfies an equation between

and

in which

is not isolated.

To differentiate an implicit function

with respect to

Differentiate both sides of the equation.
Solve for
y
′
.

To differentiate

use the following formula:

(

)

′

–

′

solution

The equation

defines

as an implicit function of

since

is not isolated. To find

′

first differentiate both sides of the equation.

(

)

′

(

)

′

(

)

′

(

)

′

(

)

′

Now, solve for

′

Make sure all terms that include

′

are isolated on one side of the equation. Then, divide by the coefficient of

′

Looking for more? Try this:

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

H.1Find derivatives of polynomials

G.2Product rule

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!