- #1

Kashmir

- 468

- 74

and

##x=f(t) ; y=g(t)##

Let the change in the function z be given by ##\Delta z=h(x+\Delta x, y+\Delta y)-h(x,y)##

We can also write the change as

##\begin{aligned} \Delta z=h &(x+\Delta x, y)-\\ & h(x, y)-h(x+\Delta x, y) \\ &+h(x+\Delta x, y+\Delta y) \end{aligned}####\Delta z=\Delta h_{y\text { constant }}+\Delta h_{x

\operatorname{constant} }##

In the limit then we have

##dz=\frac{\partial h}{\partial x} d x+\frac{\partial h}{\partial y} d y##

Is there anything wrong with this derivation?