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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{x}{y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{x}{y}

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