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人気のある微分積分 >

(\partial)/(\partial y)(3x^2y^4+1)

解

\frac{\partial}{\partial y} (3 x^{2} y^{4} + 1)

解

12 x^{2} y^{3}

解答ステップ

\frac{\partial}{\partial y} (3 x^{2} y^{4} + 1)

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} (3 x^{2} y^{4}) + \frac{\partial}{\partial y} (1)

\frac{\partial}{\partial y} (3 x^{2} y^{4}) = 12 x^{2} y^{3}

\frac{\partial}{\partial y} (1) = 0

= 12 x^{2} y^{3} + 0

簡素化

= 12 x^{2} y^{3}

人気の例

(\partial)/(\partial x)(4x^3y^2-4x^2+y^6+1)

\frac{\partial}{\partial x} (4 x^{3} y^{2} - 4 x^{2} + y^{6} + 1)

integral from 2 to 6 of x^2

\int_{2}^{6} x^{2} d x

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

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

(\partial)/(\partial x)(sqrt(9-2x^2-y^2))

\frac{\partial}{\partial x} (9 - 2 x^{2} - y^{2})

integral of 1/4 sin(2x)

\int \frac{1}{4} sin (2 x) d x