(\partial)/(\partial x)(ln(x^2+y^5))

解

\frac{\partial}{\partial x} (ln (x^{2} + y^{5}))

\frac{2 x}{x ^{2} + y ^{5}}

解答ステップ

\frac{\partial}{\partial x} (ln (x^{2} + y^{5}))

y

を定数として扱う

連鎖法則を適用:

\frac{1}{x ^{2} + y ^{5}} \frac{\partial}{\partial x} (x^{2} + y^{5})

= \frac{1}{x ^{2} + y ^{5}} \frac{\partial}{\partial x} (x^{2} + y^{5})

\frac{\partial}{\partial x} (x^{2} + y^{5}) = 2 x

= \frac{1}{x ^{2} + y ^{5}} \cdot 2 x

簡素化

\frac{1}{x ^{2} + y ^{5}} \cdot 2 x : \frac{2 x}{x ^{2} + y ^{5}}

= \frac{2 x}{x ^{2} + y ^{5}}