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

The answer to (\partial)/(\partial x)(ln(x^{0.6}y^{0.4})) is (0.6)/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{0.6}{x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\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}}

Simplify

\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}

What is (\partial)/(\partial x)(ln(x^{0.6}y^{0.4})) ?
The answer to (\partial)/(\partial x)(ln(x^{0.6}y^{0.4})) is (0.6)/x