(\partial)/(\partial x)((3x^5-7)/(4x))

解

\frac{\partial}{\partial x} (\frac{3 x ^{5} - 7}{4 x})

\frac{12 x ^{5} + 7}{4 x ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{3 x ^{5} - 7}{4 x})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{4} \frac{\partial}{\partial x} (\frac{3 x ^{5} - 7}{x})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{4} \cdot \frac{\frac{\partial}{\partial x} ( 3 x ^{5} - 7 ) x - \frac{\partial}{\partial x} ( x ) ( 3 x ^{5} - 7 )}{x ^{2}}

\frac{\partial}{\partial x} (3 x^{5} - 7) = 15 x^{4}

\frac{\partial}{\partial x} (x) = 1

= \frac{1}{4} \cdot \frac{15 x ^{4} x - 1 \cdot ( 3 x ^{5} - 7 )}{x ^{2}}

簡素化

\frac{1}{4} \cdot \frac{15 x ^{4} x - 1 \cdot ( 3 x ^{5} - 7 )}{x ^{2}} : \frac{12 x ^{5} + 7}{4 x ^{2}}

= \frac{12 x ^{5} + 7}{4 x ^{2}}