We have a funcion of 2 variables $z = g(x,y)$. And $x = cos(t)$,$y = sin(t)$. Find all partial derivatives
is it right that $$\frac{∂z}{∂x}=\frac{∂}{∂x}g(x,y)*(x)'_x=\frac{∂}{∂x}g(x,y)$$ $$\frac{∂z}{∂y}=\frac{∂}{∂y}g(x,y)_y*(y)'_y=\frac{∂}{∂y}g(x,y)$$ $$\frac{∂z}{∂t}=\frac{∂z}{∂x}\frac{∂x}{∂t} + \frac{∂z}{∂y}\frac{∂y}{∂t} = \frac{∂}{∂x}g(x,y)*(-sin(t)) + \frac{∂}{∂y}g(x,y)*cos(t)$$