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人気のある微分積分 >

(\partial)/(\partial x)(3xy^2+20x^2y^3)

解

\frac{\partial}{\partial x} (3 x y^{2} + 20 x^{2} y^{3})

解

3 y^{2} + 40 y^{3} x

解答ステップ

\frac{\partial}{\partial x} (3 x y^{2} + 20 x^{2} y^{3})

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} (3 x y^{2}) + \frac{\partial}{\partial x} (20 x^{2} y^{3})

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

\frac{\partial}{\partial x} (20 x^{2} y^{3}) = 40 y^{3} x

= 3 y^{2} + 40 y^{3} x

人気の例

y^{''}+2y^'+2y=0,y(pi/4)=2,y^'(pi/4)=-2

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (\frac{π}{4}) = 2, y^{^{'}} (\frac{π}{4}) = - 2

integral of (3x^2+17x+32)/(x^3+8x^2+16x)

\int \frac{3 x ^{2} + 17 x + 32}{x ^{3} + 8 x ^{2} + 16 x} d x

integral of (x+1)\sqrt[3]{x+2}

\int (x + 1) 3 x + 2 d x

(d^4)/(dx^4)(11e^{x^2})

\frac{d ^{4}}{d x ^{4}} (11 e^{x^{2}})

derivative of 2x^3-7x^2+3x-2

\frac{d}{d x} (2 x^{3} - 7 x^{2} + 3 x - 2)