Question #2584b

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Answer 1 · 2017-04-11T06:32:34

Let $y = f(x)$ so here , $dy/dx$ = 2 $cotx$ and it is explained as shown below :-

Given that

$y = ln((sinx)^2)$

Now differentiate both sides with respect to $x$ using Chain Rule successively, we get :-

$dy/dx = 1/(sinx)^2.d/dx((sinx)^2)$

$dy/dx = 1/((sinx)^2).(2sinx).d/dx(sinx)$

$dy/dx = 1/((sinx)^2).(2sinx).cosx$

$dy/dx = (1/sinx).2cosx$

$dy/dx = 2.(cosx/sinx)$

$dy/dx = 2cotx$

enter image source here

This is the graph of $y = ln((sinx)^2)$