To differentiate a monomial is quite simple:

• $\frac{d}{dx}x^n~=~nx^{n-1}$
Once we can differentiate a monomial, we recognise a few simple rules about differentiation:

• $\frac{d}{dx}\big(f(x)+g(x)\big)~=~\frac{d}{dx}f(x)~+~\frac{d}{dx}g(x)$
• $\frac{d}{dx}af(x)~=~a~\frac{d}{dx}f(x)$
With those rules we can differentiate a polynomial.

This is part of differential calculus.
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