Question

$$if \quad u \quad = \left(\frac{\left(\arctan \left(xy\right)\right)}{\left(\sqrt{1+x^2+y^2}\right)}\right)$$
prove $$\frac{\partial{u}}{\partial{x}}=\frac{y}{(1+x^2)(\sqrt{1+x^2+y^2}}$$

Answer 1

i got $$\frac{\frac{y}{y^2x^2+1}\sqrt{1+x^2+y^2}-\frac{x}{\sqrt{1+x^2+y^2}}\arctan \left(xy\right)}{\left(\sqrt{1+x^2+y^2}\right)^2}$$ using quotient rule

Answer 2

college stuff :{

Answer 3

It looks like what `you got` is \(\rm u\) not \(\rm u_x\).
Notice that \(\rm u\) is the first derivative with respect to x, yes?

Answer 4

first partial*

Answer 5

Hmm, second derivative is going to be a bit of work :[
I gotta head to class unfortunately.

Answer 6

sorry!! I've entered differential operator wrongly. the question is corrected now.