Simplifying Partial Derivatives: Solving for d/dx in x = x1 + x2

[phrygian]

Homework Statement

I have a problem where x = x1 + x2, and I need to relate d/dx to d/dx1 and d/dx2 somehow.

Homework Equations

The Attempt at a Solution

I'm guessing there is a simple way to do this that I have just forgotten, I know how to find dx, but how can I find d/dx?

Thanks for the help

 

[tiny-tim]

hi phrygian!

if y = f(x) and x = u + v,

then ∂f/∂u = df/dx ∂x/∂u

(basically because ∂/∂u means treating v as a constant)

 

[HallsofIvy]

Chain rule for functions of multiple variables:
$$\frac{dy}{dx}= \frac{\partial y}{\partial x_1}\frac{dx_1}{dx}+ \frac{\partial y}{\partial x_2}\frac{dx_2}{dx}$$