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

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SUMMARY

The discussion focuses on the application of the chain rule in multivariable calculus, specifically for the function z=f(x,y) where x = r*cos(theta) and y = r*sin(theta). The derived formulas for the first partial derivatives are 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). These expressions illustrate how to compute the partial derivatives of z with respect to x and y using the chain rule, emphasizing the relationships between the variables.

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QuantumPixel
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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.
 
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