What is the first d/(du)(ln(ucos(v))) ?

The first d/(du)(ln(ucos(v))) is 1/u

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d/(du)(ln(ucos(v)))

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

\frac{1}{u}

Solution steps

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

Treat

v

as a constant

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{u cos ( v )} cos (v) : \frac{1}{u}

= \frac{1}{u}

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