What is (\partial)/(\partial u)(ln(ucos(v))) ?

The answer to (\partial)/(\partial u)(ln(ucos(v))) is 1/u

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(\partial)/(\partial u)(ln(ucos(v)))

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

\frac{1}{u}

Solution steps

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

Treat

v

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial 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}

d er i v a t i v e 5 x e^{x}

\int \frac{2}{2 - e ^{x}} d x

\int sin^{4} (u) d u

\frac{d}{d x} (8 x - 2 x^{3})

\frac{d}{d x} (\frac{3 x}{1 - x})

What is (\partial)/(\partial u)(ln(ucos(v))) ?
The answer to (\partial)/(\partial u)(ln(ucos(v))) is 1/u