Consider z=f(x,y) where x = r*cos(theta) and y = r*sin(theta)

[QuantumPixel]

Use the chain rule to show that

dz/dx = (cos(theta) * dz/dr) - (1/r * sin(theta) dz/dtheta) and

dz/dy = (sin(theta) dz/dr) + 1/r * cos(theta) dz/dtheta)

where dz/dx, dz/dr, dz/dtheta, and dz/dy and first partial derivatives.

Saw this a textbook the other day and I did not understand it.

 

[CompuChip]

The question starts with "Use the chain rule to show that dz/dx = ..."
What does the chain rule tell you about dz/dx?