How do you find the derivative of #1/(1+x^2)#?

1 Answer
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

22
Euan S. Share
Jul 19, 2016

Answer:

#-(2x)/(1+x^2)^2#

Explanation:

Two straightforward ways.

#color(blue)("Method One")#

Rewrite as #(1+x^2)^(-1)# and use the power and chain rules:

#h'(x) = -(1+x^2)^(-2)*2x = -(2x)/(1+x^2)^2#

#color(blue)("Method Two")#

Use the quotient rule:

#d/(dx)((f(x))/(g(x))) = (f'(x)g(x) - f(x)g'(x))/(g(x))^2#

#h'(x) = (0 - 2x)/(1+x^2)^2 = -(2x)/(1+x^2)^2#

Was this helpful? Let the contributor know!
1500
Trending questions
Impact of this question
12493 views around the world
You can reuse this answer
Creative Commons License