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

The d/(du)(sqrt(uv)) is (sqrt(v))/(2sqrt(u))

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

The first d/(du)(sqrt(uv)) is (sqrt(v))/(2sqrt(u))

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

\frac{v}{2 u}

Solution steps

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

Treat

v

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 uv} v

Simplify

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

= \frac{v}{2 u}

\int 7 x^{\frac{3}{4}} d x

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

\int \frac{1}{x ^{2} 324 - x ^{2}} d x

\int cos (9 x) cos (3 x) d x

What is the d/(du)(sqrt(uv)) ?
The d/(du)(sqrt(uv)) is (sqrt(v))/(2sqrt(u))
What is the first d/(du)(sqrt(uv)) ?
The first d/(du)(sqrt(uv)) is (sqrt(v))/(2sqrt(u))