Testwiki:List of hoaxes on Wikipedia/Fermat differentiation

Template:Orphan 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:

$F_x[f(x)]=f^{\prime }(x)\cdot \sum _{i=1}^{d(f(x))+1}{(}_{f^{\prime }(i)}{C}_{f^{\prime }(i-1)}),$

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

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

$F(x){=}_{f(x)}{C}_{f^{\prime }(x)}.$

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 $F_x[f(x)]=68(1)+34=102$.

References

• Calculus Abbott, P. and Neill, Hugh (Contemporary Books 2003) ISBN 9780071421287
• Advanced Calculus Demystified Bachman, (Mc-Graw Hill 2007) ISBN 9780071481212

[[Category:Differential calculus]]