Notation Question

[Jason76]

This is about calculus notation, not taking a derivative.

1#

\(\displaystyle f'(x) = \dfrac{d}{dx}[x^{2}] - \dfrac{d}{dx}[x]\) - I know this is right.

OR


# 2

\(\displaystyle f'(x) = \dfrac{dy}{dx}[x^{2}] - \dfrac{dy}{dx}[x]\)

OR


# 3

\(\displaystyle \dfrac{dy}{dx} = \dfrac{dy}{dx}[x^{2}] - \dfrac{dy}{dx}[x]\)

OR

# 4

\(\displaystyle \dfrac{dy}{dx} = \dfrac{d}{dx}[x^{2}] - \dfrac{d}{dx}[x]\)

 

[DrPhil]

This is about calculus notation, not taking a derivative.

1#

\(\displaystyle f'(x) = \dfrac{d}{dx}[x^{2}] - \dfrac{d}{dx}[x]\) - I know this is right.

OR


# 2

\(\displaystyle f'(x) = \dfrac{dy}{dx}[x^{2}] - \dfrac{dy}{dx}[x]\)

OR


# 3

\(\displaystyle \dfrac{dy}{dx} = \dfrac{dy}{dx}[x^{2}] - \dfrac{dy}{dx}[x]\)

OR

# 4

\(\displaystyle \dfrac{dy}{dx} = \dfrac{d}{dx}[x^{2}] - \dfrac{d}{dx}[x]\)

If #1 is preceded by the function definition, \(\displaystyle f(x) = x^2 - x\), it is ok.

If #4 is preceded by the function definition, \(\displaystyle y = x^2 - x\), it is ok.

The other two show (x^2 - x) being multiplied by a function (dy/dx). Not at all related to the operator (d/dx) operating on (x^2 - x).

\(\displaystyle \dfrac{\mathrm d}{\mathrm d x}\) is an operator

\(\displaystyle \dfrac{\mathrm d y}{\mathrm d x}\) is the function resulting when \(\displaystyle \dfrac{\mathrm d}{\mathrm d x}\) has operated on \(\displaystyle y\).

 

[Jason76]

If #1 is preceded by the function definition, \(\displaystyle f(x) = x^2 - x\), it is ok.

If #4 is preceded by the function definition, \(\displaystyle y = x^2 - x\), it is ok.

The other two show (x^2 - x) being multiplied by a function (dy/dx). Not at all related to the operator (d/dx) operating on (x^2 - x).

\(\displaystyle \dfrac{\mathrm d}{\mathrm d x}\) is an operator

\(\displaystyle \dfrac{\mathrm d y}{\mathrm d x}\) is the function resulting when \(\displaystyle \dfrac{\mathrm d}{\mathrm d x}\) has operated on \(\displaystyle y\).

ok, thanks.