What is (\partial)/(\partial y)(ln(x^3y)) ?

The answer to (\partial)/(\partial y)(ln(x^3y)) 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^3y))

\frac{\partial}{\partial y} (ln (x^{3} y))

\frac{1}{y}

Solution steps

\frac{\partial}{\partial y} (ln (x^{3} y))

Treat

x

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{x ^{3} y} x^{3}

Simplify

\frac{1}{x ^{3} y} x^{3} : \frac{1}{y}

= \frac{1}{y}

\frac{\partial}{\partial h} (\frac{4}{3} π r^{2} h)

\frac{d}{d x} ((e^{2 x} + 1)^{l n (x)})

\int \frac{3}{1 + 4 x ^{2}} d x

\int 3 x^{2} (2 x^{2} - 5) d x

\int (\frac{6}{x}) d x

What is (\partial)/(\partial y)(ln(x^3y)) ?
The answer to (\partial)/(\partial y)(ln(x^3y)) is 1/y