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

The d/(du)(sqrt(u/v)) is 1/(2sqrt(u)\sqrt{v)}

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

The first d/(du)(sqrt(u/v)) is 1/(2sqrt(u)\sqrt{v)}

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

\frac{1}{2 u v}

Solution steps

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

Treat

v

as a constant

Apply the chain rule:

\frac{1}{2 \frac{u}{v}} \frac{d}{d u} (\frac{u}{v})

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

\frac{d}{d u} (\frac{u}{v}) = \frac{1}{v}

= \frac{1}{2 \frac{u}{v}} \cdot \frac{1}{v}

Simplify

\frac{1}{2 \frac{u}{v}} \cdot \frac{1}{v} : \frac{1}{2 u v}

= \frac{1}{2 u v}

f (x) = 1 + sin^{2} (x)

\int sec (t) (6 sec (t) + 7 tan (t)) d t

\frac{d}{d x} (\frac{7}{x ^{2} + 1})

\int x^{3} x^{2} + 32 d x

\frac{d}{d x} (3 cos (x) + 2 sin (x))

What is the d/(du)(sqrt(u/v)) ?
The d/(du)(sqrt(u/v)) is 1/(2sqrt(u)\sqrt{v)}
What is the first d/(du)(sqrt(u/v)) ?
The first d/(du)(sqrt(u/v)) is 1/(2sqrt(u)\sqrt{v)}