`\color{green} ✍️` Let `f : D →R,` `D ⊂ R,` be a given function and let `y = f (x).`
`\color{green} ✍️` Let `Δx` denote a small increment in `x.` Recall that the increment in `y` corresponding to the increment in `x,` denoted by `Δy,` is given by `color{blue}{Δy = f (x + Δx) – f (x).}`
We define the following
(i) The differential of `x,` denoted by `dx,` is defined by `dx = Δx.`
(ii) The differential of `y,` denoted by `dy,` is defined by `dy = f′(x) dx` or
`color{red}{dy = ( (dy)/(dx) ) Δx}`
`\color{green} ✍️` In case `dx = Δx` is relatively small when compared with `x,`
`dy` is a good approximation of `Δy` and we denote it by `dy ≈ Δy.`
`=>` For geometrical meaning of `Δx, Δy, dx` and `dy,` one may refer to Fig.
`\color{green} ✍️` Let `f : D →R,` `D ⊂ R,` be a given function and let `y = f (x).`
`\color{green} ✍️` Let `Δx` denote a small increment in `x.` Recall that the increment in `y` corresponding to the increment in `x,` denoted by `Δy,` is given by `color{blue}{Δy = f (x + Δx) – f (x).}`
We define the following
(i) The differential of `x,` denoted by `dx,` is defined by `dx = Δx.`
(ii) The differential of `y,` denoted by `dy,` is defined by `dy = f′(x) dx` or
`color{red}{dy = ( (dy)/(dx) ) Δx}`
`\color{green} ✍️` In case `dx = Δx` is relatively small when compared with `x,`
`dy` is a good approximation of `Δy` and we denote it by `dy ≈ Δy.`
`=>` For geometrical meaning of `Δx, Δy, dx` and `dy,` one may refer to Fig.