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

The answer to (\partial)/(\partial x)(-3x*sqrt(xy)) is -(9sqrt(x)sqrt(y))/2

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

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

- \frac{9 x y}{2}

Solution steps

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

Simplify

- 3 x x y : - 3 x^{\frac{3}{2}} y

= \frac{\partial}{\partial x} (- 3 x^{\frac{3}{2}} y)

Treat

y

as a constant

Take the constant out:

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

= - 3 y \frac{\partial}{\partial x} (x^{\frac{3}{2}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - 3 y \frac{3}{2} x^{\frac{3}{2} - 1}

Simplify

- 3 y \frac{3}{2} x^{\frac{3}{2} - 1} : - \frac{9 x y}{2}

= - \frac{9 x y}{2}

f (x) = 1 + 2 x

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

y^{^{''}} - 5 y^{^{'}} - 6 y = 0

\int 51 - 14 x - x^{2} d x

\int \frac{x ^{3} - 8}{x ^{11}} d x

What is (\partial)/(\partial x)(-3x*sqrt(xy)) ?
The answer to (\partial)/(\partial x)(-3x*sqrt(xy)) is -(9sqrt(x)sqrt(y))/2