" If "y=e^(tan x)," prove that "(cos^(2)x)(d^(2)y)/(dx^(2))-(1+sin2x)*(dy)/(dx)=0

Find the second order derivative of the following functions If y = e^(tan x) , prove that cos^2 x(d^2 y)/(dx^2) - (1 +sin 2x) (dy)/(dx) = 0

If y= e^(tan x) then show that, (cos^(2)x) (d^(2)y)/(dx^(2))- (1+ sin 2x) (dy)/(dx)=0

If y=tan^(-1)x, prove that (1+x^(2))(d^(2)y)/(dx^(2))(2x)(dy)/(dx)=0

If y=e^tanx then prove that: cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0

If y=e^tanx then prove that: cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0

If y=tan^(-1)x, prove that (1+x^(2))(d^(2)y)/(dx^(2))+2x(dy)/(dx)=0

If y=sin^(-1)x, prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)=0

If logy=tan^(-1)x , prove that : (1+x^(2)) (d^(2)y)/(dx^(2))+(2x-1)(dy)/(dx)=0

If y=e^(mtan^(-1)x) , prove that : (1+x^(2))(d^(2)y)/(dx^(2))+(2x-m)dy/dx=0 .

If y=e^(m)sin^((-1)x), prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-m^(2)y=0