1. Oct 11, 2015

### shanepitts

What is the difference between partial derivatives and gradients, if there is any?

I'm asking because I need to derive a function " f (T,P) " for air convection; where T is temperature and P is pressure and both are variables in this case.

Thanks

2. Oct 11, 2015

### micromass

A gradient is the matrix containing all the partial derivatives.

3. Oct 12, 2015

### HallsofIvy

For a function of three variables, grad $F(x,y,z)= \nabla F(x, y, z)= \frac{\partial F}{\partial x}\vec{i}+ \frac{\partial F}{\partial y}dy\vec{j}+ \frac{\partial F}{\partial z}\vec{j}$. In particular, the differential, $dF= \frac{\partial F}{\partial x}dx+ \frac{\partial F}{\partial y}dy+ \frac{\partial F}{\partial z}dz$, can be thought of as the dot product of $\nabla F$ and $dx\vec{i}+ dy\vec{j}+ dz\vec{k}$.

4. Oct 16, 2015

### GiuseppeR7

partial derivatives are "limits" meanwhile the gradient is an operator.