(\partial)/(\partial x)(sqrt(x^2+y^3))

解

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

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

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

\frac{1}{2 x ^{2} + y ^{3}} \frac{\partial}{\partial x} (x^{2} + y^{3})

= \frac{1}{2 x ^{2} + y ^{3}} \frac{\partial}{\partial x} (x^{2} + y^{3})

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

= \frac{1}{2 x ^{2} + y ^{3}} \cdot 2 x

簡素化

\frac{1}{2 x ^{2} + y ^{3}} \cdot 2 x : \frac{x}{x ^{2} + y ^{3}}

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