Y = 1/tanx find the dy/dx value

1.	Y = 1/tanx find the dy/dx value
Answer» $\large{ \pink{ \bold{y = \frac{1}{ \tan(x) } }}} \\ \\$ $\large{ \bold{y = \frac{ \ \cos(x) }{ \ \sin(x) } }} \\ \\$ ${{ \bold{ \frac{dy}{dx} = \frac{ \sin(x) ( - \sin(x) ) - \cos(x) \cos(x) }{ { \sin(x) }^{2} }}}} \\ \\$ $\large{ { \bold{ \frac{dy}{dx} = \frac{ - { \sin(x) }^{2} - { \cos(x) }^{2} }{ { \sin(x) }^{2} } }}} \\$ $\large{ { \bold{\frac{dy}{dx} = - 1 - { \cot(x) }^{2} }}}$ $\large{ { \bold{\frac{dy}{dx} = - 1(1 + { \cot(x) }^{2} }}} \\ \\$ $\large{ \purple{ \bold{ \frac{dy}{dx} = - { \csc(x) }^{2} }}} \\ \\$ PLEASE MARK ME AS BRAINLIST

Answer»

$\large{ \pink{ \bold{y = \frac{1}{ \tan(x) } }}} \\ \\$