What is (\partial)/(\partial x)(xsqrt(xy)) ?

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

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(\partial)/(\partial x)(xsqrt(xy))

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

\frac{3 x y}{2}

Solution steps

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

Simplify

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

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{3 x y}{2}

\frac{d}{d x} (\frac{x - 1}{2})

\frac{\partial}{\partial x} (\frac{90}{6 + x ^{2} + y ^{2}})

\int \frac{1}{3 x ^{2}} d x

\int cot (θ) d θ

\int (x (3 x - x) + (e^{e x} + 8)) d x

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