Wikipedia:List of hoaxes on Wikipedia/Fermat differentiation

Fermat differentiation is a type of differentiation. The Fermat derivative was first defined by Pierre de Fermat and resulted from his work in combinatorics. The Fermat derivative is written as $$F_x[f(x)]$$ and is defined for polynomials as:


 * $$F_x[f(x)]=f'(x) \cdot \sum_{i=1}^{d(f(x))+1}(_{f'(i)}C_{f'(i-1)}),\,$$

where $$d(f(x))$$ is the degree of $$f(x)$$.

The Fermat derivative measures the rate of change of the Fermat equation


 * $$F(x)=_{f(x)}C_{f'(x)}.\,$$

For example, let $$f(x)=x^2+x+1$$. The Fermat derivative is therefore $$F_x[x^2+x+1]=(2x+1) \cdot (3+10+21)=68x+34$$. The corresponding Fermat equation is therefore $$F(x)=_{x^2+x+1}C_{2x+1}$$. The rate of change at point $$(x, F(x))$$ is equal to $$F_x[f(x)]$$, which is $$68x+34$$. For example, at $$x=1$$, the rate of change of $$F(x)$$ is $$F_x[f(x)]=68(1)+34=102$$.