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人気のある微分積分 >

(\partial)/(\partial y)(y/x+4x)

解

\frac{\partial}{\partial y} (\frac{y}{x} + 4 x)

解

\frac{1}{x}

解答ステップ

\frac{\partial}{\partial y} (\frac{y}{x} + 4 x)

x

を定数として扱う

和/差の法則を適用:

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

= \frac{\partial}{\partial y} (\frac{y}{x}) + \frac{\partial}{\partial y} (4 x)

\frac{\partial}{\partial y} (\frac{y}{x}) = \frac{1}{x}

\frac{\partial}{\partial y} (4 x) = 0

= \frac{1}{x} + 0

簡素化

= \frac{1}{x}

人気の例

integral of (x^2+x^5)\sqrt[3]{x^6+2x^3}

\int (x^{2} + x^{5}) 3 x^{6} + 2 x^{3} d x

derivative-\sqrt[3]{x^5}

d er i v a t i v e - 3 x^{5}

derivative of arcsec(3x+2)

\frac{d}{d x} (arcsec (3 x + 2))

limit as x approaches (7pi)/2-of sec(x)

x \to \frac{7 π}{2} - lim (sec (x))

tangent f(x)=(2x)/(3-4x^3),\at x= 1/2

t an g e n t f (x) = \frac{2 x}{3 - 4 x ^{3}}, at x = \frac{1}{2}