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人気のある微分積分 >

derivative of x+sqrt(xy)

解

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

解

1 + \frac{y + x \frac{d y}{d x}}{2 x y}

解答ステップ

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

和/差の法則を適用:

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

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

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

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

= 1 + \frac{y + x \frac{d y}{d x}}{2 x y}

人気の例

sum from n=1 to infinity of 5/(n+1)

n = 1 \sum \infty \frac{5}{n + 1}

integral from 0 to 1 of (3t-1)^{50}

\int_{0}^{1} (3 t - 1)^{50} d t

limit as x approaches infinity of x/4

x \to \infty lim (\frac{x}{4})

limit as x approaches 0 of x/(x^2-3x)

x \to 0 lim (\frac{x}{x ^{2} - 3 x})

(\partial)/(\partial y)((7y)/(x^5))

\frac{\partial}{\partial y} (\frac{7 y}{x ^{5}})