What is the d/(dv)(sqrt(u*v)) ?

The d/(dv)(sqrt(u*v)) is (sqrt(u))/(2sqrt(v))

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

The first d/(dv)(sqrt(u*v)) is (sqrt(u))/(2sqrt(v))

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

\frac{u}{2 v}

Solution steps

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

Treat

u

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 uv} u

Simplify

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

= \frac{u}{2 v}

What is the d/(dv)(sqrt(u*v)) ?
The d/(dv)(sqrt(u*v)) is (sqrt(u))/(2sqrt(v))
What is the first d/(dv)(sqrt(u*v)) ?
The first d/(dv)(sqrt(u*v)) is (sqrt(u))/(2sqrt(v))