IXL - Find higher derivatives of rational and radical functions (Calculus practice)

Find the second derivative of the function.

(

)

′′

(

)

ref_doc_title.

Learn with an example

question

Find the second derivative of the function.

(

)

–

′′

(

)

key idea

The second derivative of

(

)

is the derivative of

′

(

)

The second derivative is written

′′

(

)

Power rule

is a real number, the derivative of

is:

(

)

′

–

Laws of exponents

m
x
n
=
x
n
m
x
a
x
b
=
x
a
–
b

solution

To find the second derivative

′′

(

)

you need to know the first derivative

′

(

)

So, start by taking the derivative of

(

)

to find

′

(

)

Rewrite each term of

(

)

as a constant times a power of

This makes it easier to take the derivative.

(

)

–

Now you can use the power rule.

′

(

)

(

–

)

′

(

–

)

′

–

(

–

)

′

(

–

)

–

(

–

)

(

–

)

–

(

–

)

–

Now take the derivative of

′

(

)

to find

′′

(

)

′′

(

)

(

–

)

′

–

(

–

)

′

(

–

)

′

–

(

–

)

(

–

)

–

(

–

)

(

–

)

–

So,

′′

(

)

–

Looking for more? Try this:

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Teacher tools

Work it out

Not feeling ready yet? These can help:

G.5Power rule II

J.1Find higher derivatives of polynomials

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