Let be a space of all polynomials (with real coefficients) of degree at most 3. Let be the linear transformation given by taking the derivative of a polynomial.

That is

let be the standard basis of .

Find the matrix of with respect to the standard basis.

I'm sure that this isn't too difficult, but I can't get my head around how to start it. I decided to find D by letting it be the transformation to get from the standard basis to the derivative.

so

So . But I have a feeling that it's not at all that simple.

Any input is greatly appreciated.

Thanks in advance,