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

解

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

9 x^{2} y + \frac{4}{x ^{2}}

解答ステップ

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

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

\frac{\partial}{\partial x} (3 x^{3} y) = 9 y x^{2}

\frac{\partial}{\partial x} (\frac{4}{x}) = - \frac{4}{x ^{2}}

\frac{\partial}{\partial x} (2 y^{\frac{1}{2}}) = 0

= 9 y x^{2} - (- \frac{4}{x ^{2}}) + 0

簡素化

= 9 x^{2} y + \frac{4}{x ^{2}}