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

1. Jul 30, 2011

### newyorkcity

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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.

2. Jul 30, 2011

### ehild

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

$$tan(\alpha+\beta)=\frac{tan(\alpha)+tan(\beta)}{1-tan(\alpha)tan(\beta)}$$