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

The answer to (\partial)/(\partial y)(ln((x+y)/(x-y))) is (2x)/((x+y)(x-y))

Popular >

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

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

\frac{2 x}{( x + y ) ( x - y )}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2 x}{( x + y ) ( x - y )}

f (x) = \frac{7}{x}, at x = 2 or, x = 7

\int \frac{2 cos ( x )}{sin ( x )} d x

\frac{d}{d x} (x^{2} + 4 y, 3 x)

\int_{0}^{\frac{π}{2}} cos^{3} (15 x) d x

\frac{d}{d x} (11 arctan (x))

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