Question

What's difference between \(\dfrac{\text{d}}{\text{d}x}\) and \( \dfrac{∂}{∂x}\ \)?

Answer 1

one is a partial derivative

Answer 2

the first one is differentiation w.r.t x
the second one is partial differentiation w.r.t. x

Answer 3

What's the difference? They seem like they work the same way. Exactly what's the difference?

Answer 4

lets say f(x,y) = x^2* y

Answer 5

partial diff w.r.t x, u get 2xy

Answer 6

u take y as constant and diff w.r.t x

Answer 7

if your a partial differentiating with respect to one variable in a multivariable problem, you treat the other variables as constants when differentiating.

Answer 8

\[\frac{d}{dx}\]
acts on a function of a single variable. Namely, x.
\[\frac{\partial }{\partial x}\]
acts on a function of more than one variable. For example:
\[f(x,y,z)\]

Answer 9

What is "w.r.t?"

Answer 10

if you diff w.r.t x, you will need to do implicit differentiation

Answer 11

with respect to

Answer 12

though, you cant do implicit differentiatin for a function that is f(x,y) partial implicit differentiation is fine

Answer 13

I see so differentiation treats other variable as variable and particle differentiation treats other variable as constant?

Answer 14

And in what situation will partial differentiation be useful?

Answer 15

yes. but you cant use both on the same function.
partial differentiation works for functions where the variables are not mutually exclusive

Answer 16

as in f(x,y)

Answer 17

d/dx is for functions where the variables are mutually exclusive. as in f(x) or f(y)

Answer 18

you can d/dx an f(y) function but u cant d/dx an f(x,y) function