What is the first derivative of x^2 1/2 ?

The first derivative of x^2 1/2 is x

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derivative of x^2 1/2

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

x

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

= x

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

\int \frac{x ^{2} + 1}{x - 1} d x

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\frac{d}{d x} ((6 x^{0.5} - x^{2})^{2})

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