∂z∂φ=zxcosα+zysinα\frac{\partial z}{\partial \varphi} = z_x \cos\alpha + z_y \sin\alpha∂φ∂z=zxcosα+zysinα ∂2z∂φ2=zxxcosα⋅cosα+zyysinα⋅sinα=zxxcos2α+zyysin2α\frac{\partial^2 z}{\partial \varphi^2} = z_{xx} \cos\alpha \cdot \cos\alpha + z_{yy} \sin\alpha \cdot \sin\alpha = z_{xx} \cos^2\alpha + z_{yy} \sin^2\alpha∂φ2∂2z=zxxcosα⋅cosα+zyysinα⋅sinα=zxxcos2α+zyysin2α ∂z∂ρ=−zxsinα+zycosα\frac{\partial z}{\partial \rho} = -z_x \sin\alpha + z_y \cos\alpha∂ρ∂z=−zxsinα+zycosα ∂2z∂ρ2=zxxsin2α+zyycos2α\frac{\partial^2 z}{\partial \rho^2} = z_{xx} \sin^2\alpha + z_{yy} \cos^2\alpha∂ρ2∂2z=zxxsin2α+zyycos2α 左辺 =zφφ+zρρ=zxxcos2α+zyysin2α+zxxsin2α+zyycos2α= z_{\varphi\varphi} + z_{\rho\rho} = z_{xx} \cos^2\alpha + z_{yy} \sin^2\alpha + z_{xx} \sin^2\alpha + z_{yy} \cos^2\alpha=zφφ+zρρ=zxxcos2α+zyysin2α+zxxsin2α+zyycos2α =zxx+zyy== z_{xx} + z_{yy} ==zxx+zyy= 右辺