Derivative Help: Defining ((d/dx)-1)y & Proving Property

[annoymage]

Homework Statement

let y be the function of x

how do i define ((d/dx)-1)y
is it dy/dx -y ? if so, which definition should i know to proof this property? help help

 

[hunt_mat]

You have defined a differential operator:
$$T=\frac{d}{dx}-1$$
It is a linear operator, this is clear but it can be proven.

 

[annoymage]

differential operator thanks, I'm looking forward to that, but before that,

what should i do to resolve ((d/dx)-1)x^2

how to do that?

2x-x^2?

 

[hunt_mat]

Correct! Your differential operator says that given a function I should differentiate it and take away the original function.

Mat