What is (\partial)/(\partial x)(10sqrt(xy)) ?

The answer to (\partial)/(\partial x)(10sqrt(xy)) is (5sqrt(y))/(sqrt(x))

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(\partial)/(\partial x)(10sqrt(xy))

\frac{\partial}{\partial x} (10 x y)

\frac{5 y}{x}

Solution steps

\frac{\partial}{\partial x} (10 x y)

Treat

y

as a constant

Take the constant out:

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

= 10 \frac{\partial}{\partial x} (x y)

Apply the chain rule:

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

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

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

= 10 \cdot \frac{1}{2 x y} y

Simplify

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

= \frac{5 y}{x}

\frac{d}{d x} (x^{2} - 4)

\frac{d}{d x} (sin (x) sin (y) sin (x + y))

x \to 2 lim (x^{3} f (x))

n = 1 \sum \infty \frac{( - 1 ) ^{n}}{5 ( 2 ^{n + 2} )}

x \to 1 + lim (\frac{7}{1 - x})

What is (\partial)/(\partial x)(10sqrt(xy)) ?
The answer to (\partial)/(\partial x)(10sqrt(xy)) is (5sqrt(y))/(sqrt(x))