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}

x \to 0 lim (\frac{sin ^{7} ( x )}{x})

y^{^{''}} + 4 y = \frac{4}{cos ( 2 t )}

\int - t e^{- t} d t

\int (8 + x^{3})^{5} (3 x^{2}) d x

f (x) = \frac{1}{5 x ^{2} + 4 x}

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