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

The answer to (\partial)/(\partial x)(sqrt(x)+ln(5x+y)) is 1/(2sqrt(x))+5/(5x+y)

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

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

\frac{1}{2 x} + \frac{5}{5 x + y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x) = \frac{1}{2 x}

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

= \frac{1}{2 x} + \frac{5}{5 x + y}

What is (\partial)/(\partial x)(sqrt(x)+ln(5x+y)) ?
The answer to (\partial)/(\partial x)(sqrt(x)+ln(5x+y)) is 1/(2sqrt(x))+5/(5x+y)