Question

Помогите решить самостоятельную

Answer 1

$z=f(x,y)\ \ ,\ \ x(u,v)\ \ ,\ \ y=y(u,v)\\\\\dfrac{\partial z}{\partial u}=\dfrac{\partial z}{\partial x}\cdot \dfrac{\partial x}{\partial u}+\dfrac{\partial z}{\partial y}\cdot \dfrac{\partial y}{\partial u}\ \ ,\ \ \ \dfrac{\partial z}{\partial v}=\dfrac{\partial z}{\partial x}\cdot \dfrac{\partial x}{\partial v}+\dfrac{\partial z}{\partial y}\cdot \dfrac{\partial y}{\partial v}\\\\\\z=(x+1)\cdot lny\ \ ,\ \ x=u^2-3v\ ,\ y=uv-\sqrt{v}\\\\\\\dfrac{\partial z}{\partial u}=lny\cdot 2u+\dfrac{x+1}{y}\cdot v$

$\dfrac{\partial z}{\partial v}=lny\cdot (-3)+\dfrac{x+1}{y}\cdot \Big(u-\dfrac{1}{2\sqrt{v}}\Big)=-3\, lny+\dfrac{(x+1)\cdot (2u\sqrt{v}-1)}{2y\, \sqrt{v}}$