Formula:61

Digital Library of Mathematical Functions ID 1.4.E13

${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}x}^{n}}f(g(x))=\sum\left(\frac{n!}{m_{1}!m_{2}!\cdots m_{n}!}\right)f^{(k)}(g(x))\*\left(\frac{g^{\prime}(x)}{1!}\right)^{m_{1}}\left(\frac{g^{\prime\prime}(x)}{2!}\right)^{m_{2}}\dots\left(\frac{g^{(n)}(x)}{n!}\right)^{m_{n}},}}$

Symbols List

• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle k}}$: integer
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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