If y =(tan^–1x)², show that

Given: y =(tan^–1x)²

To show:

given y =(tan^–1x)²

Now applying first derivative with respect to x, we get

Now applying the power rule of differentiation, we get

And we know differentiation of , substituting this in above equation, we get

Now applying second derivative with respect to x, we get

Taking out the constant term, we get

Now applying the quotient rule of differentiation, we get

And we know differentiation of , substituting this in above equation, we get

Now applying the sum rule of differentiation, we get

Now we will consider the LHS,

Now we will substitute the values from equation (i) and (ii)in above equation, we get

⇒=(2[1-2x(tan^-1x)])+2x(2(tan^-1x))

⇒=(2[1-2x(tan^-1x)]+ 2x(tan^-1x))

⇒=2=RHS

Hence proved