If `y=e^("sin"^(-1)x)andz=e^(-"cos"^(-1)x)`, prove that `dy/(dz)=e^(pi//2)`.

If y=e^(sin^(-1)x)+e^(cos^(-1)x),0ltxlt1 , then

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

If y=e^xcosx , prove that (d^2y)/(dx^2)=2\ e^xcos(x+pi/2) .

If y=e^xcosx , prove that (dy)/(dx)=sqrt(2)\ e^xcos(x+pi/4)

If y=e^x+e^(-x) , prove that (dy)/(dx)=sqrt(y^2-4)

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

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

If y=e^(x^(e^x))+x^(e^(e^x))+e^(x^(x^e)) , prove that (dy)/(dx)=e^(x^(e^x)) . x^(e^x){(e^x)/x+e^x.logx}+x^(e^(e^x)).e^(e^x){1/x+e^xdotlogx}+e^(x^(x^e)).x^(x^e).x^(e-1){1+elogx}

If e^x+e^y=e^(x+y) , prove that (dy)/(dx)+e^(y-x)=0

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