What is the d/(dv)(tan(u/v)) ?

The d/(dv)(tan(u/v)) is -(usec^2(u/v))/(v^2)

What is the first d/(dv)(tan(u/v)) ?

The first d/(dv)(tan(u/v)) is -(usec^2(u/v))/(v^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Treat

u

as a constant

Apply the chain rule:

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

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

\frac{d}{d 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}}

What is the d/(dv)(tan(u/v)) ?
The d/(dv)(tan(u/v)) is -(usec^2(u/v))/(v^2)
What is the first d/(dv)(tan(u/v)) ?
The first d/(dv)(tan(u/v)) is -(usec^2(u/v))/(v^2)