Partial derivative of arctan(u/v) with respect to u

[kasse]

Homework Statement

Differentiate f = arctan(u/v) with respect to u

The Attempt at a Solution

Using the chain rule

f_u = (1/(1 + (u/v)²)) * 1/v = 1/(v + u²/v)

The solutions manual says v/(u² + v²)

What is my mistake?

 

[hotcommodity]

Multiply the top and bottom of your answer by "v" and see what you get