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人気のある微分積分 >

(\partial)/(\partial y)(1/y)

解

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

解

- \frac{1}{y ^{2}}

解答ステップ

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

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

= \frac{\partial}{\partial y} (y^{- 1})

乗の法則を適用:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - 1 \cdot y^{- 1 - 1}

簡素化

- 1 \cdot y^{- 1 - 1} : - \frac{1}{y ^{2}}

= - \frac{1}{y ^{2}}

人気の例

limit as x approaches 1 of cos(1/(x-1))

x \to 1 lim (cos (\frac{1}{x - 1}))

tangent y=x^3-3x+3,(3,21)

t an g e n t y = x^{3} - 3 x + 3, (3, 21)

limit as x approaches pi/2 of (sec(x))/(sec(3x))

x \to \frac{π}{2} lim (\frac{sec ( x )}{sec ( 3 x )})

tangent f(x)=3+4x^2-2x^3,\at x=a

t an g e n t f (x) = 3 + 4 x^{2} - 2 x^{3}, at x = a

(y+4)y^'=2xy+4y,y(2)=1

(y + 4) y^{^{'}} = 2 x y + 4 y, y (2) = 1