What is (\partial)/(\partial x)(ln(x+y)-5y) ?

The answer to (\partial)/(\partial x)(ln(x+y)-5y) is 1/(x+y)

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(\partial)/(\partial x)(ln(x+y)-5y)

\frac{\partial}{\partial x} (ln (x + y) - 5 y)

\frac{1}{x + y}

Solution steps

\frac{\partial}{\partial x} (ln (x + y) - 5 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (ln (x + y)) - \frac{\partial}{\partial x} (5 y)

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

\frac{\partial}{\partial x} (5 y) = 0

= \frac{1}{x + y} - 0

Simplify

= \frac{1}{x + y}

\frac{d}{d x} ((x + 3)^{x})

\frac{d}{d x} (x^{5 e^{x}})

ln (\frac{x}{2} - 3), [7, 9]

\int_{0}^{3} \int_{0}^{y} e^{- y^{2}} d x d y

\int x^{2} + 3 x + C d x

What is (\partial)/(\partial x)(ln(x+y)-5y) ?
The answer to (\partial)/(\partial x)(ln(x+y)-5y) is 1/(x+y)