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人気のある微分積分 >

(\partial)/(\partial y)(2xy^3+3)

解

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

解

6 x y^{2}

解答ステップ

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

x

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

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

\frac{\partial}{\partial y} (3) = 0

= 6 x y^{2} + 0

簡素化

= 6 x y^{2}

人気の例

tangent 4/(x+2)

t an g e n t \frac{4}{x + 2}

integral of (4t^3-3t^2+4t)/(t^2+1)

\int \frac{4 t ^{3} - 3 t ^{2} + 4 t}{t ^{2} + 1} d t

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

(\partial)/(\partial x)(xe^y+ye^x)

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

integral from 0 to 1 of (49)/(x^5)

\int_{0}^{1} \frac{49}{x ^{5}} d x