(\partial)/(\partial x)(ln(x^3+y)-z)

解

\frac{\partial}{\partial x} (ln (x^{3} + y) - z)

\frac{3 x ^{2}}{x ^{3} + y}

解答ステップ

\frac{\partial}{\partial x} (ln (x^{3} + y) - z)

y, z

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} (ln (x^{3} + y)) - \frac{\partial}{\partial x} (z)

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

\frac{\partial}{\partial x} (z) = 0

= \frac{3 x ^{2}}{x ^{3} + y} - 0

簡素化

= \frac{3 x ^{2}}{x ^{3} + y}