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

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

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

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

y + \frac{1}{x + y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{d}{d x} (sin^{l n (x)} (3 x))

\int sin (a t) d t

\frac{d}{d x} (e^{3 x} + 10 e^{2 x})

t^{2} y^{^{'}} + 3 t y + 2 t^{3} = 0

(e^{y} + 6 x) d x + (x e^{y}) d y = 0

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