derivative of e^y+y/x

解答

\frac{d}{d x} (e^{y} + \frac{y}{x})

e^{y} \frac{d y}{d x} + \frac{x \frac{d y}{d x} - y}{x ^{2}}

求解步骤

\frac{d}{d x} (e^{y} + \frac{y}{x})

使用微分加减法定则:

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

= \frac{d}{d x} (e^{y}) + \frac{d}{d x} (\frac{y}{x})

\frac{d}{d x} (e^{y}) = e^{y} \frac{d y}{d x}

\frac{d}{d x} (\frac{y}{x}) = \frac{x \frac{d y}{d x} - y}{x ^{2}}

= e^{y} \frac{d y}{d x} + \frac{x \frac{d y}{d x} - y}{x ^{2}}

x \to - 2 lim (\frac{2 x ^{2} + 3 x}{x - 3})

\frac{d}{d x} (arcsin (8 x) + arccos (8 x))

y^{^{''}} - 6 y^{^{'}} - 16 y = 0

\frac{d}{d x} (4 x^{0.75} \cdot (240 - 2 x)^{0.5})

\int_{- 3}^{- 1} \frac{5}{x ^{4}} d x