Find the derivative of arctan(6x)

[jumbogala]

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?

 

[lanedance]

if you make the subsitition u(x) = 6x

then you have
$$\frac{d}{dx} arctan(u(x))$$

so you need to use the chain rule...

 

[jumbogala]

I can't read your equation...

 

[jumbogala]

Okay, so:

1/(u^2 +1) multiplied by the derivative of u?

 

[HallsofIvy]

Yes. And since u= 6x, its derivative is ?

 

[jumbogala]

6/(36x^2 +1)?

Thank you!