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人気のある微分積分 >

derivative of x*y^2

解

\frac{d}{d x} (x \cdot y^{2})

解

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

解答ステップ

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = y^{2}

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

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

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

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

簡素化

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

人気の例

laplacetransform t^{5/2}

l a pl a ce t r an s f or m t^{\frac{5}{2}}

integral of x^4e^{(x^5)}

\int x^{4} e^{(x^{5})} d x

limit as x approaches 5 of (x^2+1)/(x-5)

x \to 5 lim (\frac{x ^{2} + 1}{x - 5})

inverselaplace 1/(s^2-2s+3)

in v erse l a pl a ce \frac{1}{s ^{2} - 2 s + 3}

(\partial)/(\partial x)(3x^2-2x+6y^2+2y+2)

\frac{\partial}{\partial x} (3 x^{2} - 2 x + 6 y^{2} + 2 y + 2)