What is (\partial)/(\partial y)(ln(x^8y)) ?

The answer to (\partial)/(\partial y)(ln(x^8y)) is 1/y

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(ln(x^8y))

\frac{\partial}{\partial y} (ln (x^{8} y))

\frac{1}{y}

Solution steps

\frac{\partial}{\partial y} (ln (x^{8} y))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{x ^{8} y} \frac{\partial}{\partial y} (x^{8} y)

= \frac{1}{x ^{8} y} \frac{\partial}{\partial y} (x^{8} y)

\frac{\partial}{\partial y} (x^{8} y) = x^{8}

= \frac{1}{x ^{8} y} x^{8}

Simplify

\frac{1}{x ^{8} y} x^{8} : \frac{1}{y}

= \frac{1}{y}

\frac{\partial}{\partial x} (x^{\frac{1}{4}} \cdot y^{\frac{3}{4}})

x \to π - lim (4 x)

\frac{\partial}{\partial x} (6 x^{- 3} - 8 x^{- 5})

\frac{d}{d x} (500 x - \frac{x ^{2}}{ln ( x + 300 )})

\frac{d}{d x} ((3 x^{2} - 6 x + 10) (x^{3}))

What is (\partial)/(\partial y)(ln(x^8y)) ?
The answer to (\partial)/(\partial y)(ln(x^8y)) is 1/y