What is (\partial)/(\partial x)(2x^{3/2}) ?

The answer to (\partial)/(\partial x)(2x^{3/2}) is 3x^{1/2}

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(\partial)/(\partial x)(2x^{3/2})

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

y = - x^{2} + 6 x, y = x^{2} - 2 x

\frac{3}{5 x ^{4}}

4 y^{^{''}} + 3 y^{^{'}} + 7 y = 0

x y^{^{'}} + y = x^{2} + 1

\frac{d}{d x} ((3 cos (2 x) + sin (3 x))^{2})

What is (\partial)/(\partial x)(2x^{3/2}) ?
The answer to (\partial)/(\partial x)(2x^{3/2}) is 3x^{1/2}