(\partial)/(\partial x)(2+xln(xy-7))

解答

\frac{\partial}{\partial x} (2 + x ln (x y - 7))

\frac{x y}{x y - 7} + ln (x y - 7)

求解步骤

\frac{\partial}{\partial x} (2 + x ln (x y - 7))

将

y

视为常数

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (2) + \frac{\partial}{\partial x} (x ln (x y - 7))

\frac{\partial}{\partial x} (2) = 0

\frac{\partial}{\partial x} (x ln (x y - 7)) = ln (y x - 7) + \frac{y x}{y x - 7}

= 0 + ln (y x - 7) + \frac{y x}{y x - 7}

化简

= \frac{x y}{x y - 7} + ln (x y - 7)

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

\int \frac{3 x ^{2} + 8 x - 12}{x ^{3} + 7 x + 12 x} d x

\int \frac{3 ^{x + 2}}{4 ^{x - 1}} d x

\int x cos (6 x) d x

\int x^{- 2} e^{\frac{1}{x}} d x