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}

f (t) = r^{2} + 6 r - 3

(3.1) (6.3)

x \to 3 + lim (\frac{x ^{2}}{3 x - 9})

- 2 x^{4} + 2 x^{3} - x^{2} + x

y = 7 e^{x}

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