Q. 205.0( 1 Vote )

# 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 Rate this question :

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