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

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

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

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

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(x)^{^{'}}

\frac{1}{2 x}

Solution steps

(x)^{'}

Apply radical rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{1}{2 x}

\int \frac{180 x ^{2}}{( 3 x + 1 ) ( 3 x + 5 ) ( x + 2 )} d x

f (x) = cos (ln (x))

\int_{0}^{4} \frac{1}{x ^{2}} d x

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

\int - 2 cos (t) d t