derivative of (x-1(ln(x)))

解答

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

ln (x) + \frac{x - 1}{x}

求解步骤

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

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x - 1, g = ln (x)

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

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

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

= 1 \cdot ln (x) + \frac{1}{x} (x - 1)

化简

1 \cdot ln (x) + \frac{1}{x} (x - 1) : ln (x) + \frac{x - 1}{x}

= ln (x) + \frac{x - 1}{x}

\frac{\partial}{\partial x} (3 sin (4 x))

\frac{d}{d x} (- \frac{x ^{4}}{4})

\frac{d y}{y ^{3}} = x^{- 2} d x

\int \frac{3 ^{x}}{1 + 9 ^{x}} d x

d er i v a t i v e - \frac{12}{x ^{5}}