What is (\partial)/(\partial y)(ln(x^2+3xy)) ?

The answer to (\partial)/(\partial y)(ln(x^2+3xy)) is 3/(x+3y)

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^2+3xy))

\frac{\partial}{\partial y} (ln (x^{2} + 3 x y))

\frac{3}{x + 3 y}

Solution steps

\frac{\partial}{\partial y} (ln (x^{2} + 3 x y))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{x ^{2} + 3 x y} \frac{\partial}{\partial y} (x^{2} + 3 x y)

= \frac{1}{x ^{2} + 3 x y} \frac{\partial}{\partial y} (x^{2} + 3 x y)

\frac{\partial}{\partial y} (x^{2} + 3 x y) = 3 x

= \frac{1}{x ^{2} + 3 x y} \cdot 3 x

Simplify

\frac{1}{x ^{2} + 3 x y} \cdot 3 x : \frac{3}{x + 3 y}

= \frac{3}{x + 3 y}

f (x) = x^{2} e^{x}

\int x 81 - x^{2} d x

\int_{0}^{12} 2 π x (12 x - x^{2}) d x

(u - u) (u + u)

x^{2} + 2 x - 3

What is (\partial)/(\partial y)(ln(x^2+3xy)) ?
The answer to (\partial)/(\partial y)(ln(x^2+3xy)) is 3/(x+3y)