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## Homework Statement

if z = x

^{2}+ 2y

^{2}, x = r cos θ , y = r sin θ , find the partial derivative

[itex]\left(\frac{\partial z}{\partial \theta}\right)_{x}[/itex]

## Homework Equations

z = x

^{2}+ 2y

^{2}

x = r cos θ

y = r sin θ

## The Attempt at a Solution

The textbook says that the equation should be re-written to include only the variables θ and x, and then differentiated with respect to θ.

Substituting y = r sin θ :

z = x

^{2}+ 2r

^{2}sin

^{2}θ

then [itex]\left(\frac{\partial z}{\partial \theta}\right)_{x}[/itex] = 4r

^{2}sin θ cos θ

However the solutions in the book give

[itex]\left(\frac{\partial z}{\partial \theta}\right)_{x}[/itex] = 4r

^{2}tan θ

What am I missing here?

Thanks in advance.