Thread: Partial Derivative vs. Normal Derivative

1. Partial Derivative vs. Normal Derivative

Hi,

On my HP-50G calculator, there are three ways to calculate the derivative (HP-50G differentiation tutorial):
1. $\partial$
2. DERIV(function, variable)
3. DERVX(function)

All of which can be used for symbolic differentiation. With the partial derivative, isn't that basically a fancy way of denoting differentiation in higher dimensions (just so it isn't confused with 1D derivatives symbolically)? So even though I use the partial derivative for simple $\frac{dy}{dx}$ calculations, which would be represented as $\frac{\partial y}{\partial x}$ on my HP-50G calculator, it still is a typical derivative because it is operating at a single-variable level?

2. Re: Partial Derivative vs. Normal Derivative

It looks like $\partial$ and DERIV are the same thing. You need to give it an expression and a variable; it then takes the partial derivative of the expression with respect to the variable. The third one, DERIVX, is the same thing except it assumes your variable is x, so you only need to give it an expression. It is true that when you have a function of only x, the partial derivative with respect to x is the same as the derivative with respect to x.

Try taking the derivative of something like $x^2\sin{y}$ using all three methods and see what happens.

- Hollywood

3. Re: Partial Derivative vs. Normal Derivative

Originally Posted by hollywood
Try taking the derivative of something like $x^2\sin{y}$ using all three methods and see what happens.

- Hollywood
They all gave the same answer: $2x\sin(y)$.

4. Re: Partial Derivative vs. Normal Derivative

Good. But, with $f(x,y)= x^2 sin(y)$, $\partial f/\partial y$ and Deriv(f, y) should be the same but different from DerivX(f)

5. Re: Partial Derivative vs. Normal Derivative

Originally Posted by HallsofIvy
Good. But, with $f(x,y)= x^2 sin(y)$, $\partial f/\partial y$ and Deriv(f, y) should be the same but different from DerivX(f)
You are right - when I differentiate over $y$ it gives $x^2 \cos y$. It also does that for $\frac{\partial}{\partial y} x^2 \sin y$. So basically, the DERIV and $\partial$ functions are essentially the same because they hold the other variable that is not being differentiated constant (the $x^2$). Thus, they are both specifically partial derivative functions.