# What is the derivative of #Tan^-1 (y/x)#?

##### 3 Answers

#### Answer:

#### Explanation:

Using the chain rule on the left side:

Using the product rule on the right side:

#### Answer:

#### Explanation:

This problem needs a slight prerequisite of chain rule, and quotient rule.

Thus,

It really depends upon what you are doing, and which independent variables matter to you.

Let

Using the **Quotient Rule** and **Implicit Differentiation** on

The partial derivatives are therefore:

#{(z_x = - y/(x^2 + y^2)),(z_y = x/(x^2 + y^2)):}#

But if

# dz/dx = ( x \ dy/dx - y \ dx/dx) /(x^2+y^2) #

Which is the total derivative wrt

# dz/dx = z_y dy/dx + z_x#