What is the (sqrt(y))^' ?

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

What is the first (sqrt(y))^' ?

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

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(y)^{^{'}}

\frac{1}{2 y}

Solution steps

(y)^{'}

Apply radical rule:

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

= (y^{\frac{1}{2}})^{^{'}}

Apply the Power Rule:

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

= \frac{1}{2} y^{\frac{1}{2} - 1}

Simplify

\frac{1}{2} y^{\frac{1}{2} - 1} : \frac{1}{2 y}

= \frac{1}{2 y}

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