What is the (2sqrt(x))^' ?

The (2sqrt(x))^' is 1/(sqrt(x))

What is the first (2sqrt(x))^' ?

The first (2sqrt(x))^' is 1/(sqrt(x))

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(2 x)^{^{'}}

\frac{1}{x}

Solution steps

(2 x)^{'}

Take the constant out:

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

= 2 (x)^{^{'}}

Apply radical rule:

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

= 2 (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}{x}