Question

Find solution derivatives of 1/tan(x/a)

Answer 1

d/dx(1/tan(x/a))=d/dx(cot(x/a))=-cosec^2(x/a).(1/a)
=-cosec^2(x/a)/a
we get the above by applying chain rule.

Answer 2

$\frac{1}{tan{\frac{x}{a}}}=cot\frac{x}{a}\\\\\\y=cot\frac{x}{a}\\\\differenttiate\\\\\frac{dy}{dx}=-cosec^2\frac{x}{a}.\frac{1}{a}$