(\partial)/(\partial x)(2xy^5+3x^2y+x^2)

解答

\frac{\partial}{\partial x} (2 x y^{5} + 3 x^{2} y + x^{2})

2 y^{5} + 6 y x + 2 x

求解步骤

\frac{\partial}{\partial x} (2 x y^{5} + 3 x^{2} y + x^{2})

将

y

视为常数

使用微分加减法定则:

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

= \frac{\partial}{\partial x} (2 x y^{5}) + \frac{\partial}{\partial x} (3 x^{2} y) + \frac{\partial}{\partial x} (x^{2})

\frac{\partial}{\partial x} (2 x y^{5}) = 2 y^{5}

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

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

= 2 y^{5} + 6 y x + 2 x

y^{^{''}} + 9 y = 6 tan (3 x)

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