Find the derivative of arctan(6x)

  • Thread starter jumbogala
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  • #1
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Homework Statement


Find the derivative of arctan(6x).


Homework Equations





The Attempt at a Solution


Ok, I know the derivative of arctan(x) is 1/(x^2 + 1).

So I am trying to make the substitution u = 6x.

Then the derivative of arctan(u) should be 1/(u^2 + 1)... and therefore 1/(36x^2 +1).

But that's not right... what am I doing wrong?
 

Answers and Replies

  • #2
lanedance
Homework Helper
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if you make the subsitition u(x) = 6x

then you have
[tex] \frac{d}{dx} arctan(u(x)) [/tex]

so you need to use the chain rule...
 
  • #3
423
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I can't read your equation...
 
  • #4
423
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Okay, so:

1/(u^2 +1) multiplied by the derivative of u?
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
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Yes. And since u= 6x, its derivative is ?
 
  • #6
423
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6/(36x^2 +1)?

Thank you!
 

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