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)#