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

The answer to (\partial)/(\partial x)(5ln(sqrt(xy))) is 5/(2x)

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(\partial)/(\partial x)(5ln(sqrt(xy)))

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

\frac{5}{2 x}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

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

Simplify

5 \cdot \frac{1}{x y} \cdot \frac{1}{2 x y} y : \frac{5}{2 x}

= \frac{5}{2 x}

x^{^{''}} + 20 x^{^{'}} + 500 x = 12

y = x^{2} (1 - 2 x)

\int_{0}^{4} x - x + 2 d x

x \to 1 lim (\frac{- 2}{x - 1})

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

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