What is (\partial)/(\partial x)(2x^{1/2}) ?

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

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(\partial)/(\partial x)(2x^{1/2})

\frac{\partial}{\partial x} (2 x^{\frac{1}{2}})

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

Solution steps

\frac{\partial}{\partial x} (2 x^{\frac{1}{2}})

Take the constant out:

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

= 2 \frac{\partial}{\partial x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

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

Simplify

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

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

\frac{d}{d y} (4 y^{3})

\int_{0}^{9} (2 x^{3} + 1) d x

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

\int (x^{2} + 1)^{- 1} d x

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