# Total derivative and partial derivative

1. Aug 18, 2014

### mikengan

can anyone tell me the difference of application of total derivative and partial derivative in physics?
i still can't figure it out after searching on the internet

2. Aug 18, 2014

### ShayanJ

A total derivative tells you how a quantity changes if another quantity changes, regardless on the kind of dependence of the first quantity on the second. But for a partial derivative, the second quantity should only appear explicitly in the expression giving the first quantity.
For example consider $y(x(t),t)=2x(t)^2+bt^2$, we'll have:
$\frac{\partial y}{\partial t}=2bt \\ \frac{d y}{dt}=4x(t) \frac{dx(t)}{dt}+2bt$