What is (\partial)/(\partial x)(3sqrt(xy)) ?

The answer to (\partial)/(\partial x)(3sqrt(xy)) is (3sqrt(y))/(2sqrt(x))

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(\partial)/(\partial x)(3sqrt(xy))

\frac{\partial}{\partial x} (3 x y)

\frac{3 y}{2 x}

Solution steps

\frac{\partial}{\partial x} (3 x y)

Treat

y

as a constant

Take the constant out:

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

= 3 \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

= 3 \cdot \frac{1}{2 x y} y

Simplify

3 \cdot \frac{1}{2 x y} y : \frac{3 y}{2 x}

= \frac{3 y}{2 x}

\int_{1}^{4} - 7 t ln (t) d t

\frac{d}{d x} (\frac{2 x ^{3} + 4}{x ^{2} - 4 x + 1})

x \to 0 lim (ln (tan (7 x)))

\int \frac{16 x ^{2}}{16 x ^{2} + 25} d x

\int \frac{x ^{2} + 4 x - 1}{x ^{3} - x} d x

What is (\partial)/(\partial x)(3sqrt(xy)) ?
The answer to (\partial)/(\partial x)(3sqrt(xy)) is (3sqrt(y))/(2sqrt(x))