derivative of 1/(x^n)

解答

\frac{d}{d x} (\frac{1}{x ^{n}})

- n x^{- n - 1}

求解步骤

\frac{d}{d x} (\frac{1}{x ^{n}})

使用指数法则:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} (x^{- n})

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - n x^{- n - 1}

d er i v a t i v e y = \frac{4 x ^{2} + 4 x + 8}{x}

\frac{\partial}{\partial x} (y - x^{2} - 7 z^{2})

t an g e n t f (x) = x^{2} + 8, at x = 2

\int e^{x} + 2 d x

x \to - \infty lim (x^{2} + 6)