derivative of x+y*ln(5-x/2)

解答

\frac{d}{d x} (x + y \cdot ln (5 - \frac{x}{2}))

1 + ln (5 - \frac{x}{2}) \frac{d y}{d x} - \frac{y}{10 - x}

求解步骤

\frac{d}{d x} (x + y ln (5 - \frac{x}{2}))

使用微分加减法定则:

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

= \frac{d x}{d x} + \frac{d}{d x} (y ln (5 - \frac{x}{2}))

\frac{d x}{d x} = 1

\frac{d}{d x} (y ln (5 - \frac{x}{2})) = ln (5 - \frac{x}{2}) \frac{d y}{d x} - \frac{y}{10 - x}

= 1 + ln (5 - \frac{x}{2}) \frac{d y}{d x} - \frac{y}{10 - x}

\frac{d}{d x} (4 x^{3} - 4 x)

d er i v a t i v e f (x) = 500 - 500 t^{- 1}

x \to - 5 lim (x)

t an g e n t \frac{4 x}{x ^{2} + 1}

\int_{0}^{8} 1 + x d x