(\partial)/(\partial x)(ln(y^{x^2}))

解

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

2 x ln (y)

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

= \frac{1}{y ^{x^{2}}} \cdot 2 y^{x^{2}} x ln (y)

簡素化

\frac{1}{y ^{x^{2}}} \cdot 2 y^{x^{2}} x ln (y) : 2 x ln (y)

= 2 x ln (y)