What is the d/(du)(sqrt(u)) ?

The d/(du)(sqrt(u)) is 1/(2sqrt(u))

What is the first d/(du)(sqrt(u)) ?

The first d/(du)(sqrt(u)) is 1/(2sqrt(u))

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\frac{d}{d u} (u)

\frac{1}{2 u}

Solution steps

\frac{d}{d u} (u)

Apply radical rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{1}{2 u}

\frac{d}{d x} ((6 x - 1) (5 x - 2)^{- 1})

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

y^{^{''}} + 4 y^{^{'}} + 5 y = - 10 x + 3 e^{- x}

x \to 3 lim (x - 2)

\int \frac{sec ^{2} ( x )}{x} d x