(\partial)/(\partial z)(ln(1+x^2+e^y+z))

解

\frac{\partial}{\partial z} (ln (1 + x^{2} + e^{y} + z))

\frac{1}{1 + x ^{2} + e ^{y} + z}

解答ステップ

\frac{\partial}{\partial z} (ln (1 + x^{2} + e^{y} + z))

x, y

を定数として扱う

連鎖法則を適用:

\frac{1}{1 + x ^{2} + e ^{y} + z} \frac{\partial}{\partial z} (1 + x^{2} + e^{y} + z)

= \frac{1}{1 + x ^{2} + e ^{y} + z} \frac{\partial}{\partial z} (1 + x^{2} + e^{y} + z)

\frac{\partial}{\partial z} (1 + x^{2} + e^{y} + z) = 1

= \frac{1}{1 + x ^{2} + e ^{y} + z} \cdot 1

簡素化

= \frac{1}{1 + x ^{2} + e ^{y} + z}