(\partial)/(\partial x)(ln(x^{0.6}y^{0.4}))

解答

\frac{\partial}{\partial x} (ln (x^{0.6} y^{0.4}))

\frac{0.6}{x}

求解步骤

\frac{\partial}{\partial x} (ln (x^{0.6} y^{0.4}))

将

y

视为常数

使用连锁律:

\frac{1}{x ^{0.6} y ^{0.4}} \frac{\partial}{\partial x} (x^{0.6} y^{0.4})

= \frac{1}{x ^{0.6} y ^{0.4}} \frac{\partial}{\partial x} (x^{0.6} y^{0.4})

\frac{\partial}{\partial x} (x^{0.6} y^{0.4}) = \frac{0.6 y ^{0.4}}{x ^{0.4}}

= \frac{1}{x ^{0.6} y ^{0.4}} \cdot \frac{0.6 y ^{0.4}}{x ^{0.4}}

化简

\frac{1}{x ^{0.6} y ^{0.4}} \cdot \frac{0.6 y ^{0.4}}{x ^{0.4}} : \frac{0.6}{x}

= \frac{0.6}{x}

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