Differentiating an equation with 3 variables

[rich101]

Hi
So this is pretty basic but how would you differentiate u = (a^2 + b^2 + c^2) please where a, b and c are three separate, independent variables. Please.

would it be (2a+b^2+c^2)+(2b+a^2=c^2)+(2c+a^2+b^2)?

Thanks

 

[phyzguy]

Try reading this:
http://en.wikipedia.org/wiki/Partial_derivative

 

[HallsofIvy]

No, it wouldn't. First, you have to make the question clearer. Do you mean "partial derivatives" and, if so, with respect to which variable? Or do you mean the "total differential"?

If you do not know what "partial derivatives" are then you should look up "partial derivatives" in a Calculus text.

The partial derivatives of $u = a^2 + b^2 + c^2$ with respect to a, b, and c are:
$$\frac{\partial u}{\partial a}= 2a$$
$$\frac{\partial u}{\partial b}= 2b$$
$$\frac{\partial u}{\partial c}= 2c$$

The "total differential" would be du= 2ada+ 2bdb+ 2cdc