wtf (1 Viewer)

[Average Boreduser]

does any1 know what a partial derivative is? how tf does one even work i am so confused

 

[WeiWeiMan]

i'm sure there are good explanations online
while i haven't rly looked at it in a while i'm fairly sure partial derivative is just differentiating with respect to a certain variable and allowing all the other variables to act like constants

 

[Average Boreduser]

i'm sure there are good explanations online
while i haven't rly looked at it in a while i'm fairly sure partial derivative is just differentiating with respect to a certain variable and allowing all the other variables to act like constants

yeah but how does that work geometrically tho- like wtf is this gradient supposed to represent here

 

[liamkk112]

does any1 know what a partial derivative is? how tf does one even work i am so confused

lol not really relevant to hsc but:

say we define a function z= f(x,y). then the partial derivative of f with respect to x represents how much the slope of f changes when you change x, at a particular y that we hold constant. similarly partial derivative of f with respect to y represents how much the slope of f changes when you change y, at a particular x that we hold constant. think of partial f of x as taking a slice the graph of z = f(x,y) at a particular y value. then, we basically get the regular derivative, but of the particular 2-d slice of the graph we took.

yeah but how does that work geometrically tho- like wtf is this gradient supposed to represent here

you might be getting confused because partial derivatives aren't like regular derivatives, as they don't represent how the whole graph changes, only with respect to one variable although the graph changes with two, which seems a bit backwards. this is where you need to know the gradient operator and directional derivatives.

essentially, ∇f is the vector < δf/δx, δf/δy>, it's just used for shorthand and the ∇ is called the gradient. we can also define a particular unit vector u in a certain direction, which is the direction that we want to measure the rate of change of the graph in. then, the directional derivative is given by ∇f dotted with u. there's a whole geometrical explanation for this that tbh i forgot lol it's been a while since i watched videos on multivariable calculus

 

[idkkdi]

yeah but how does that work geometrically tho- like wtf is this gradient supposed to represent here

3ds pretty visualisable. 4d and beyond give up