IXL - Find higher derivatives of logarithmic and power functions (Calculus practice)

Find

(

)

(

)

(

)

29!

28!

29!

30!

ref_doc_title.

Learn with an example

question

Find

(

)

(

)

(

)

86!

87!

86!

87!

key idea

The

derivative of

(

)

can be found by taking

derivatives in a row, starting with

(

)

The first, second, and third derivatives are written

′

(

)

′′

(

)

and

′′′

(

)

For

the

derivative is written

(

)

(

)

Factorials

A factorial is a product of the form

…

and is written

…

solution

To find

(

)

(

)

compute several derivatives in a row and look for a pattern.

(

)

′

(

)

′′

(

)

′′′

(

)

(

)

(

)

Each time a derivative is taken, the exponent decreases by 1. After taking 85 derivatives, the exponent will reach 1, and the coefficient will be the product of the integers from 85 down to 2.

(

)

(

)

…

Multiply by 1 to recognize the product is a factorial

…

Multiply by 1 to recognize the product is a factorial

86!

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Teacher tools

Work it out

Not feeling ready yet? These can help:

J.1Find higher derivatives of polynomials

J.2Find higher derivatives of rational and radical functions

J.3Find second derivatives of trigonometric, exponential, and logarithmic functions

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