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## Homework Statement

Consider z=f(x,y), where x=rcosθ and y=rsinθ

Show that [itex]\frac{\partial z}{\partial x}=\cos\theta\frac{\partial z}{\partial r}-\frac{1}{r}\sin\theta\frac{\partial z}{\partial\theta}[/itex]

## Homework Equations

## The Attempt at a Solution

Z

Connects to X and Y

X Connects to r and θ, Y Connects to r and θ

Is dz/dx not then equal to dx/dr + dx/dθ? because that is equivalent to dz/dx = r -rsinθ.

What am I doing wrong here?