Why does the derivative of arctan(4t) equal 4/(1+16t²)?

[dlikes]

Homework Statement

The Integral is arctan (4t) dt

Homework Equations

I know how to do integration by parts, but I guess I have forgotten some of the integration rules.

The Attempt at a Solution

I set ∫arctan(4t)=u, and dt=dv

I know that the derivative of arctan(x) is 1/(1+x^2), But when I differentiate arctan(4t), it comes out as 4t/(1+16t^2). Why is this? To me it seems like it should be 1/(1+4t^2). I know how to do the rest, I have the answer, I'm just not sure how they got there. Thanks for any help.

 

[gabbagabbahey]

But when I differentiate arctan(4t), it comes out as 4t/(1+16t^2). Why is this?

Because you've calculated the derivative wrong. To tell you exactly where your error is, you'll need to post your steps.