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人気のある微分積分 >

(\partial)/(\partial x)(5x^4+y^8)

解

\frac{\partial}{\partial x} (5 x^{4} + y^{8})

解

20 x^{3}

解答ステップ

\frac{\partial}{\partial x} (5 x^{4} + y^{8})

y

を定数として扱う

和/差の法則を適用:

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

= \frac{\partial}{\partial x} (5 x^{4}) + \frac{\partial}{\partial x} (y^{8})

\frac{\partial}{\partial x} (5 x^{4}) = 20 x^{3}

\frac{\partial}{\partial x} (y^{8}) = 0

= 20 x^{3} + 0

簡素化

= 20 x^{3}

人気の例

derivative of ((3x+512/(x+1))^{2/3})

\frac{d}{d x} ((\frac{3 x + 512}{x + 1})^{\frac{2}{3}})

yy^'= x/(x^2+1),y(0)=-2

y y^{^{'}} = \frac{x}{x ^{2} + 1}, y (0) = - 2

(dy)/(dx)-y/(3x)+x/(3y)=0

\frac{d y}{d x} - \frac{y}{3 x} + \frac{x}{3 y} = 0

integral of xsin^2(6x)

\int x sin^{2} (6 x) d x

derivative of 4x^3-46x^2+120x

\frac{d}{d x} (4 x^{3} - 46 x^{2} + 120 x)