Question

Como derivar cos(2x)/tan(2x)

Answer 1

Use the quotient and chain rules. If

`y = (\cos(2x))/(\tan(2x))`

then the derivative is

`(dy)/(dx) = \frac{\tan(2x) \frac d{dx}\cos(2x) - \cos(2x) \frac d{dx}\tan(2x)}{\tan^2(2x)}`

`(dy)/(dx) = \frac{\tan(2x) (-\sin(2x)) \frac d{dx}(2x) - \cos(2x)\sec^2(2x) \frac d{dx}(2x)}{\tan^2(2x)}`

`(dy)/(dx) = (-2\sin(2x)\tan(2x) - 2 \sec(2x) )/(\tan^2(2x))`

and we can rewrite this by

• multiplying by
`(\cos^2(2x))/(\cos^2(2x))`,

`(dy)/(dx) = (-2\sin^2(2x)\cos(2x) - 2 \cos(2x) )/(\sin^2(2x))`

• factorizing,

`(dy)/(dx) = -(2\cos(2x) \left(\sin^2(2x) + 1\right))/(\sin^2(2x))`

etc