derivative of (ln(x)^3)

解答

\frac{d}{d x} ((ln (x))^{3})

\frac{3 ln ^{2} ( x )}{x}

求解步骤

\frac{d}{d x} ((ln (x))^{3})

使用连锁律:

3 (ln (x))^{2} \frac{d}{d x} (ln (x))

= 3 (ln (x))^{2} \frac{d}{d x} (ln (x))

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= 3 (ln (x))^{2} \frac{1}{x}

化简

3 ln^{2} (x) \frac{1}{x} : \frac{3 ln ^{2} ( x )}{x}

= \frac{3 ln ^{2} ( x )}{x}

\frac{\partial}{\partial x} (\frac{1}{x - b})

d er i v a t i v e f (x) = \frac{( 10 - 3 x ) + 2}{2}

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

\frac{\partial}{\partial x} (x^{2} \cdot sin^{2} (yz))

a re a y = x, y = x + 6, 0 < x < 5