Çok Değişkenli Fonksiyonlarda Zincir Kuralı

Question

$$w=x^2+\ln y+\cos z$$ olmak üzere $$x=2u^2-v^2, \,\ y=u^3+v, \,\ z=u\cdot v$$ olduğuna göre $$2\cdot \frac{\partial w}{\partial u}-\frac{\partial w}{\partial v}=?$$

Answer 1

İpucu: 

$$\frac{\partial w}{\partial u}=\frac{\partial w}{\partial x}\cdot\frac{\partial x}{\partial u}+\frac{\partial w}{\partial y}\cdot\frac{\partial y}{\partial u}+\frac{\partial w}{\partial z}\cdot\frac{\partial z}{\partial u}$$

ve

$$\frac{\partial w}{\partial v}=\frac{\partial w}{\partial x}\cdot\frac{\partial x}{\partial v}+\frac{\partial w}{\partial y}\cdot\frac{\partial y}{\partial v}+\frac{\partial w}{\partial z}\cdot\frac{\partial z}{\partial v}$$

ise

$$2\cdot\frac{\partial w}{\partial u}-\frac{\partial w}{\partial v}=\ldots$$