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人気のある微分積分 >

(\partial)/(\partial y)(3x^2y^2)

解

\frac{\partial}{\partial y} (3 x^{2} y^{2})

解

6 x^{2} y

解答ステップ

\frac{\partial}{\partial y} (3 x^{2} y^{2})

x

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 x^{2} \frac{\partial}{\partial y} (y^{2})

乗の法則を適用:

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

= 3 x^{2} \cdot 2 y^{2 - 1}

簡素化

= 6 x^{2} y

人気の例

limit as x approaches 3 of 5x-1

x \to 3 lim (5 x - 1)

(dy)/(dx)=(e^x)/(2+e^x)

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

integral of (19xe^{2x})/((1+2x)^2)

\int \frac{19 x e ^{2 x}}{( 1 + 2 x ) ^{2}} d x

derivative of 6x+sin(3x)

\frac{d}{d x} (6 x + sin (3 x))

derivative of (1-x^2/(2-x^3))

\frac{d}{d x} (\frac{1 - x ^{2}}{2 - x ^{3}})