`y = 1/(x^2 + 4)` Find the derivative of the function.

Textbook Question

Chapter 2, Review - Problem 55 - Calculus of a Single Variable (10th Edition, Ron Larson).
See all solutions for this textbook.

2 Answers | Add Yours

hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

Note:- If y = x^n ; where n = constant, then dy/dx = n*x^(n-1)

Now, 

`y = 1/{(x^2) + 4}`

`Thus, y = {(x^2) + 4}^-1`

`or, y' = -1{{(x^2) + 4}^-2}*(2x)`

`or, y' = -2x/{(x^2)+4}^2`

``

loves2learn's profile pic

loves2learn | (Level 3) Salutatorian

Posted on

Using a Quotient rule,

Using a Quotient rule:

Given,

Then,

Therefore,

`y'=((0)(x^2+4)-(1)(2x))/(x^2+4)^2 `

Simplify,

`y'= (-2x)/(x^2+4)^2`

Note that you should get the same answer if you used a product rule by bringing `x^2+4` up with a negative exponent. If you don't, then check your answer because you must have made a mistake along the way.

We’ve answered 318,915 questions. We can answer yours, too.

Ask a question