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人気のある微分積分 >

derivative of x^2y^4

解

\frac{d}{d x} (x^{2} y^{4})

解

2 x y^{4} + 4 y^{3} \frac{d y}{d x} x^{2}

解答ステップ

\frac{d}{d x} (x^{2} y^{4})

積の法則を適用:

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

f = x^{2}, g = y^{4}

= \frac{d}{d x} (x^{2}) y^{4} + \frac{d}{d x} (y^{4}) x^{2}

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

\frac{d}{d x} (y^{4}) = 4 y^{3} \frac{d y}{d x}

= 2 x y^{4} + 4 y^{3} \frac{d y}{d x} x^{2}

人気の例

limit as x approaches 2 of x^2-5

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

limit as x approaches 0 of (1-e^{-x})/x

x \to 0 lim (\frac{1 - e ^{- x}}{x})

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

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

derivative e^x(x^2+1)(x+4)

d er i v a t i v e e^{x} (x^{2} + 1) (x + 4)

面積 y=-x,y=-x^2+ex

a re a y = - x, y = - x^{2} + e x