Dear friends, Please read our latest blog post for an important announcement about the website. ❤, The Socratic Team

What is the derivative of #f(x)=tan^-1(x)# ?

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

18
Jul 1, 2015

I seem to recall my professor forgetting how to deriving this. This is what I showed him:

#y = arctanx#

#tany = x#

#sec^2y (dy)/(dx) = 1#

#(dy)/(dx) = 1/(sec^2y)#

Since #tany = x/1# and #sqrt(1^2 + x^2) = sqrt(1+x^2)#, #sec^2y = (sqrt(1+x^2)/1)^2 = 1+x^2#

#=> color(blue)((dy)/(dx) = 1/(1+x^2))#

I think he originally intended to do this:

#(dy)/(dx) = 1/(sec^2y)#

#sec^2y = 1+tan^2y#

#tan^2y = x -> sec^2y = 1+x^2#

#=> (dy)/(dx) = 1/(1+x^2)#

Was this helpful? Let the contributor know!
1500
Impact of this question
8449 views around the world
You can reuse this answer
Creative Commons License