- #1
bawbag
- 13
- 1
Homework Statement
if z = x2 + 2y2 , 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 = x2 + 2y2
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 = x2 + 2r2 sin2 θ
then [itex]\left(\frac{\partial z}{\partial \theta}\right)_{x}[/itex] = 4r2sin θ cos θ
However the solutions in the book give
[itex]\left(\frac{\partial z}{\partial \theta}\right)_{x}[/itex] = 4r2 tan θ
What am I missing here?
Thanks in advance.