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)^{'}

Take the constant out:

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

= - (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}

\frac{d}{d x} (ln (arcsin (x)))

\int (\frac{- x ^{2} + x}{x ^{4}}) d x

\int 2 x - 2 x^{2} d x

f (x) = x^{2}, g (x) = 2 x

\int \frac{3}{80 - t} d t