IXL - Find derivatives of rational functions (Calculus practice)

Find the derivative of

(

)

–

′

(

)

ref_doc_title.

Learn with an example

question

Find the derivative of

(

)

–

′

(

)

key idea

When the denominator of a rational function

(

)

is a power of

you can find

′

(

)

using the power rule instead of the quotient rule.

The power rule says that if

is a real number, the derivative of

is:

(

)

′

–

Here are some basic derivative rules:

The derivative of a constant is 0:
(
c
)
′
=
0
.
The derivative of
x
is 1:
(
x
)
′
=
1
.

solution

Since

(

)

is a rational function whose denominator is a power of

you can find

′

(

)

using the power rule.

Rewrite

(

)

as a sum of fractions with only one term in the numerator. Then, use exponent laws to write each fraction as a constant multiple of exactly one power of

(

)

–

Now, you can use the power rule to find

′

(

)

′

(

)

(

–

)

′

(

–

)

′

(

–

)

′

–

(

–

)

′

(

–

)

′

Apply the power rule

–

(

–

)

(

–

)

Apply the power rule

–

Rewrite using positive exponents

–

Rewrite using positive exponents

So,

′

(

)

–

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:

G.3Quotient rule

H.1Find derivatives of polynomials

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!