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人気のある微分積分 >

derivative of y^2(2-x-x^3)

解

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

解

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

解答ステップ

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

和/差の法則を適用:

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

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

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

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

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

人気の例

derivative x^2+2

d er i v a t i v e x^{2} + 2

y^'+3y=0,y(0)=0

y^{^{'}} + 3 y = 0, y (0) = 0

(\partial)/(\partial x)(e^{(y+1)x})

\frac{\partial}{\partial x} (e^{(y + 1) x})

derivative f(x)=(x^3+9x^2+x-8)/x

d er i v a t i v e f (x) = \frac{x ^{3} + 9 x ^{2} + x - 8}{x}

(\partial)/(\partial x)(sqrt(4ax))

\frac{\partial}{\partial x} (4 a x)