" Jर्वि "(y=sin(tan^(-1)2x)," तब सिक्द कीरि ")/(dx)=(2)/((1+4x^(2))^(3/2))

If y=sin(tan^(-1)2x), prove that (dy)/(dx)=(2)/((1+4x^(2))^((3)/(2)))

If y=sin^(-1)x, show that (d^(2)y)/(dx^(2))=(1)/((1-x^(2))^(3/2))

If y=sin^(-1)x , show that (d^2y)/(dx^2)=x/((1-x^2)^(3//2))

If y= "tan"^(-1) (4x)/(1+5x^(2)) + "tan"^(-1) (2 + 3x)/(3-2x) , then prove that (dy)/(dx)= (5)/(1+25x^(2))

Statement I If y=sin^(-1)(3x-4x^(3)), then (dy)/(dx)=(3)/(sqrt(1-x^(2))) only when (-1)/(2)lexlt(1)/(2)/. Statement II sin^(-1)(3x-4x^(3)) ={(-pi-3sin^(-1)x,,-1lexle-(1)/(2),),(3sin^(-1)x,,-(1)/(2)lexle(1)/(2),),(pi-3sin^(-1)x,,(1)/(2)lexle1,):}

Statement I If y=sin^(-1)(3x-4x^(3)), then (dy)/(dx)=(3)/(sqrt(1-x^(2))) only when (-1)/(2)lexlt(1)/(2)/. Statement II sin^(-1)(3x-4x^(3)) ={(-pi-3sin^(-1)x,,-1lexle-(1)/(2),),(3sin^(-1)x,,-(1)/(2)lexle(1)/(2),),(pi-3sin^(-1)x,,(1)/(2)lexle1,):}

Statement I If y=sin^(-1)(3x-4x^(3)), then (dy)/(dx)=(3)/(sqrt(1-x^(2))) only when (-1)/(2)lexlt(1)/(2)/. Statement II sin^(-1)(3x-4x^(3)) ={(-pi-3sin^(-1)x,,-1lexle-(1)/(2),),(3sin^(-1)x,,-(1)/(2)lexle(1)/(2),),(pi-3sin^(-1)x,,(1)/(2)lexle1,):}

If x = sin (2tan ^ (- 1) 2), y = sin ((1) / (2) tan ^ (- 1) ((4) / (3))), then -