IXL - Introduction to related rates (Calculus practice)

Let

and

be functions of

with

what is

when

Write an exact, simplified answer.

ref_doc_title.

Learn with an example

question

Let

and

be functions of

with

what is

when

Write an exact, simplified answer.

solution

First, consider what information you are given and what information you are looking for. You are given

and

You are looking for

when

The equation

relates

and

Take the derivative of both sides with respect to

to get an equation that relates

and

Since

is a function of

remember that you need to use the chain rule to differentiate the right side of the equation with respect to

(

)

Differentiate both sides with respect to

(

)

Differentiate both sides with respect to

Use the chain rule

Now use this equation to find

Substitute the given information,

and

into the equation.

(

)

(

)

So,

when

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.14Find derivatives using the chain rule I

I.1Find derivatives using implicit differentiation

H.9Find derivatives using the product rule I

H.11Find derivatives using the quotient rule I

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!