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

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

Popular >

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

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

\frac{y}{x ( x + y )}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{y}{x ( x + y )}

n = 1 \sum \infty \frac{1}{( n + 2 ) ^{2}}

y = \frac{3}{16 - x}, at x = 0

\int x e^{- x (y + 1)} d x

\int \frac{( 2 x - 1 ) ^{2}}{2 x} d x

\int_{0}^{\frac{1}{2}} 1 d x

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