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

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

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

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

\frac{3 x}{2}

Solution steps

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

Apply radical rule:

n a^{m} = a^{\frac{m}{n}}

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{3 x}{2}

\frac{\partial}{\partial x} ((3 x^{2} + 5 x + 1) \cdot (y + 4))

\frac{d y}{d x} = y (x y^{3} - 1)

\frac{d}{d x} (arccsc (\frac{x + 1}{1 - x}))

y^{^{''}} + 4 y^{^{'}} + 5 y = 35 e - 4 x, y (0) = - 5, y^{^{'}} (0) = 1

\int 11 - 10 x - x^{2} d x

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