(\partial)/(\partial x)(4y(1/x-ln(x)))

解

\frac{\partial}{\partial x} (4 y (\frac{1}{x} - ln (x)))

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

解答ステップ

\frac{\partial}{\partial x} (4 y (\frac{1}{x} - ln (x)))

y

を定数として扱う

定数を除去:

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

= 4 y \frac{\partial}{\partial x} (\frac{1}{x} - ln (x))

和/差の法則を適用:

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

= 4 y (\frac{\partial}{\partial x} (\frac{1}{x}) - \frac{\partial}{\partial x} (ln (x)))

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

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

= 4 y (- \frac{1}{x ^{2}} - \frac{1}{x})