What is (\partial)/(\partial v)(tan(u/v)) ?

The answer to (\partial)/(\partial v)(tan(u/v)) is -(usec^2(u/v))/(v^2)

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(\partial)/(\partial v)(tan(u/v))

\frac{\partial}{\partial v} (tan (\frac{u}{v}))

- \frac{u sec ^{2} ( \frac{u}{v} )}{v ^{2}}

Solution steps

\frac{\partial}{\partial v} (tan (\frac{u}{v}))

Treat

u

as a constant

Apply the chain rule:

sec^{2} (\frac{u}{v}) \frac{\partial}{\partial v} (\frac{u}{v})

= sec^{2} (\frac{u}{v}) \frac{\partial}{\partial v} (\frac{u}{v})

\frac{\partial}{\partial v} (\frac{u}{v}) = - \frac{u}{v ^{2}}

= sec^{2} (\frac{u}{v}) (- \frac{u}{v ^{2}})

Simplify

sec^{2} (\frac{u}{v}) (- \frac{u}{v ^{2}}) : - \frac{u sec ^{2} ( \frac{u}{v} )}{v ^{2}}

= - \frac{u sec ^{2} ( \frac{u}{v} )}{v ^{2}}

n = 3 \sum \infty \frac{2}{n ( n + 2 )}

\int - 5 csc^{2} (x) d x

x \to - 3 + lim (\frac{x + 4}{x + 3})

x \to + (- 4) lim (∣ x + 4 ∣)

y = 3 x - 4, (2, 5)

What is (\partial)/(\partial v)(tan(u/v)) ?
The answer to (\partial)/(\partial v)(tan(u/v)) is -(usec^2(u/v))/(v^2)