What is (\partial)/(\partial x)(1/2 ln(x+y)) ?

The answer to (\partial)/(\partial x)(1/2 ln(x+y)) is 1/(2(x+y))

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(\partial)/(\partial x)(1/2 ln(x+y))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is (\partial)/(\partial x)(1/2 ln(x+y)) ?
The answer to (\partial)/(\partial x)(1/2 ln(x+y)) is 1/(2(x+y))