Question

What is the derivative of (arctan(3x))/x

Answer 1

Hey Kay :)
Do you have the derivative of arctan(x) handy?
We'll need that at some point.

Answer 2

Let's get our derivative "set up" first though,
and we'll worry about the arctangent afterwards.

Answer 3

The derivative of arctan(x) is 1/1x^2 if I'm correct

Answer 4

1/(1+x^2)
I think you made a silly typo there, ya? :)

Answer 5

Yeah

Answer 6

So we have a quotient,
we'll apply quotient rule, ya?\[\large\rm \frac{d}{dx}\frac{\arctan(3x)}{x}=\frac{\color{royalblue}{\left[\arctan(3x)\right]'}x-\arctan(3x)\color{royalblue}{\left[x\right]'}}{(x)^2}\]Understand the set up?
We have to differentiate the blue stuff.

Answer 7

I don't know if I'm supposed to do something... but I can't see it all?

Answer 8

You mean you can't see the fancy math formatted?
Hmm are you using Internet Explorer?
That browser doesn't load the plugin correctly sometimes :(

Answer 9

I'm just using internet on my samsung, thats all it says

Answer 10

I can use the draw tool instead if it's not showing up properly

Answer 11

Would using a computer maybe wrk better?

Answer 12

Ugh, website is freezing again :(

Answer 13

some of it

Answer 14

So we're using our quotient rule.