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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

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

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

y = 4 x + 48, (4, 8)

\frac{74}{s ^{2} + 1}

\int 3 cos^{3} (3 x) d x

\int_{4}^{5} x x - 4 d x

\frac{d}{d x} (- 0.5 x^{2} + 56 x + 20)

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