More Articles from Archive ~ Calcolo Differenziale

$f(x):\mathbb R\to\mathbb R$, $\displaystyle f'(x)=\frac {d\,f(x)}{d\,x}=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$ $\displaystyle \frac{d\, c}{d\, x}=0$, dove $c$ è una costante $\displaystyle \frac{d\, x}{d\, x}=1$ $\displaystyle \frac{d}{d\, x}(f(x)+cg(x))=\frac{d\,f(x)}{d\, x}+c \frac{d\,g(x)}{d\, x}$ $\displaystyle \frac{d}{d\, x}(f(x)g(x))=\frac{d\,f(x)}{d\, x} g(x)+f(x) \frac{d\,g(x)}{d\, x}$ $\displaystyle \frac{d}{d\, x}(f(g(x))=f'(g(x))g'(x)$ $\displaystyle g'(y)=\frac 1{f'(x)}$, $y=f(x)$, $x=g(y)$ $\displaystyle \frac{d}{d\, x} x^n=nx^{n-1}$ $\displaystyle \frac{d}{d\, x}f(x)^n=nf(x)^{n-1}f'(x)$ $\displaystyle \frac{d}{d\, x}\frac1{f(x)}=-\frac 1{f(x)^2}f'(x)$ $\displaystyle \frac{d}{d\, x}\sin(x)=\cos(x)$, […]

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