Question

find dy/dx if y = tanx /cotx​

Answer 1

Answer:

$\rm \dfrac{d}{dx} \bigg(\dfrac{tan \ x}{cot \ x}\bigg) = 2 \ tan \ x \sec^2 x$

Explanation:

$\sf Derivation: \\ \implies \sf \dfrac{d}{dx} \bigg( \dfrac{tan \: x}{cot \: x} \bigg) \\ \\ \sf Rewrite \: the \: expression: \\ \implies \sf \dfrac { d}{dx}(tan^2x) \\ \\ \sf Using \: the \: chain \: rule, \: we \: get : \\ \implies \sf 2 \: tan \: x \: \dfrac{d}{dx}(tanx) \\ \\ \sf Derivative \: of \: tan \: x = {sec}^{2} x : \\ \implies \sf 2 \: tan \: x \: {sec}^{2} x$

Answer 2

Refer to the attachment for the solution.

I hope this will be helpful.