Sezione 6.2

Esempi classici

\frac{d^n}{dx^n}[e^{kx}]=k^ne^{kx}

\frac{d^n}{dx^n}[\sin(kx)]=k^n\sin\!\left(kx+\frac{n\pi}{2}\right)

\frac{d^n}{dx^n}[\cos(kx)]=k^n\cos\!\left(kx+\frac{n\pi}{2}\right)

\frac{d^n}{dx^n}[x^m]=\begin{cases} m(m-1)\cdots(m-n+1)\,x^{m-n}, & n\le m\\ 0, & n>m,\ m\in\mathbb{N}_0 \end{cases}

Caricamento sezione…

Sezione 6.2

\frac{d^n}{dx^n}[e^{kx}]=k^ne^{kx}

\frac{d^n}{dx^n}[\sin(kx)]=k^n\sin\!\left(kx+\frac{n\pi}{2}\right)

\frac{d^n}{dx^n}[\cos(kx)]=k^n\cos\!\left(kx+\frac{n\pi}{2}\right)

\frac{d^n}{dx^n}[x^m]=\begin{cases} m(m-1)\cdots(m-n+1)\,x^{m-n}, & n\le m\\ 0, & n>m,\ m\in\mathbb{N}_0 \end{cases}