Understanding Partial Derivatives: A Visual Explanation

[O.J.]

OK, they're throwing pretty weird concepts to our heads in this PHY101 course. stuff like even partial derivatives that we didnt take in math. differentiating partially with respect to a single variable treating others as contants is NOT getting through my head. can someon PLEASE illustrate it for me?

 

[gammamcc]

partial derive of xyz with respect to y (say) is as if z and x are just numbers
so you get xz*1= xz.

Say you replaced every other variable with a fixed number except the var. you differentiate. It is then just regular derivatives. Remember calc 1? What is the deriv. (w/ resp. to x) of Cx^4 ...ANS> C*4*x^3. Now, change C to another variable y,z,w ...whatever.. same math.

Hope it helps.

 

[Gza]

$$E_p(k_X, k_Y) = \iint E_s(x,y)e^{i(xk_X+yk_Y)}\,dx\,dy$$

 

[duke_nemmerle]

heh, wish I knew what text you were using, I was looking for a phy101 that does exactly this(but that it does it without warning you before you enroll is pretty nasty)

 

[theperthvan]

partial derive of xyz with respect to y (say) is as if z and x are just numbers
so you get xz*1= xz.

Say you replaced every other variable with a fixed number except the var. you differentiate. It is then just regular derivatives.


Remember calc 1? What is the deriv. (w/ resp. to x) of Cx^4 ...ANS> C*4*x^3. Now, change C to another variable y,z,w ...whatever.. same math.

Hope it helps.

pretty sure he doesn't get the concept but he knows how to do it.

It's like the derivative wrt x (say) along a curve where z,y are constant. Drawing a picture will make it easy straight away. Think of a solid shape. Chop it into two pieces. The rate of change along the edge is kind of doing a partial derivative.