Derivatives of arctan((x+y)/(1-xy))

[newyorkcity]

Homework Statement

Find all second partial derivatives of
z=arctan((x+y)/(1-xy))

Homework Equations

d/dx of arctan(x) is 1/(1+x^2)

The Attempt at a Solution

Not sure how to proceed... I don't want the answer, just an idea as to how to move forward.

My attempt at finding the first derivative...

z'=(1/(1+(x+y/(1-xy)) * (x(1-xy) - (x+y(-y)) / (1-xy)^2

Is this correct? If it is, I honestly don't know how to find the second derivative...

On another note, can someone tell me how I can use math notation instead of plain text, to make the equations and such easier to read? Thanks guys.

 

[ehild]

Take care of the parentheses. Check the derivative of the arctan function.

To make your task easier, remember the addition formula :
$$tan(\alpha+\beta)=\frac{tan(\alpha)+tan(\beta)}{1-tan(\alpha)tan(\beta)}$$
Can you write the function z(x,y) in a simpler form?
As for Math notations, go to "advanced" and click on the 'Σ'.
ehild