derivative of (x^{n-1}/n)

解答

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

\frac{x ^{n - 2} ( n - 1 )}{n}

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用幂法则:

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

= \frac{1}{n} (n - 1) x^{n - 1 - 1}

化简

\frac{1}{n} (n - 1) x^{n - 1 - 1} : \frac{x ^{n - 2} ( n - 1 )}{n}

= \frac{x ^{n - 2} ( n - 1 )}{n}

n = 0 \sum \infty \frac{n ^{3}}{5 ^{n}}

\frac{\partial}{\partial x} (2 x^{3} y + sin (x^{2}))

t an g e n t f (x) = \frac{4 x}{x ^{2} - 5}, (3, 3)

x \to 7 lim (\frac{x + 2}{x - 7})

\int \frac{e ^{3 x} + 1}{e ^{2 x}} d x