# Partial derivative

## Homework Statement

Hey, i ve got problem with a few partial derivative problems.

1.I have a function T(x,t)
Prove that dT/dt=∂T/∂t +∂T/∂x dx/dt

2.Let u(x,y) and y(x,u) be continous, differentiable functions.
Prove that
∂u/∂z=∂u/∂z ∂y/∂z

3
Let r(q1,q2,...qn) be a function of place depending on n coordinates.
Show that ∂r/∂q=derivative of r/derivative of q
,

## The Attempt at a Solution

Well, the first one i tried to prove chain rule for partial derivatives but i failed. I also cannot find one in the Web.

Second comes from Leibniz notation for derivatives - but again I cant prove it myself or find a prove.

Third- well i dont have a clue.

$$\frac{df}{dt}= \frac{\partial f}{\partial x}\frac{dx}{dt}+ \frac{\partial f}{\partial y}\frac{dy}{dt}$$