Arctan dy/dx

[racuna]

How do you apply differentiation to
H(x)=(1+x^2)arctan x?

 

[jsbeckton]

product rule

 

[racuna]

do you have to put it in terms of
1/1+x^2, and if so, how do you do that?

 

[jsbeckton]

first distribute to get rid of () then us f' g + g' f

 

[racuna]

ok, thanks!

 

[Unco]

I'd imagine differentiating arctan(x) might be troubling you.

Hint: Let tan(theta) = x

(You can draw a right-angled triangle to show theta = arctan(x).)

Differentiate implicitly and use the right-angled triangle to get it back in terms of x.

See how you go.

Edit: Ok never mind, it appears you know its derivative already.

 

[jsbeckton]

it should look like: dy/dx arctan(x) + x^2 arctan(x)

use the product rule on the part in bold.

 

[jsbeckton]

hint the derivitive of arctan is 1/1+x^2.......see where this is going.....