(Q)/((23))" If "y=e^(a cos^(-1)x),-1<=x<=1," show that "(1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-a^(2)y=0

If y= e^(sin^(-1)x) and z=e^(-cos^(-1)x) , prove that the value of (dy)/(dz) independent of x.

If y = e^(m cos^(-1) x) (1-x^2)y_2-xy_1 = m^2y

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=e^(tanx) , then (cos^2x)y2-(1+sin2x)y1=0

Let A=[(cos^(- 1)x,cos^(- 1)y,cos^(- 1)z),(cos^(- 1)y,cos^(- 1)z,cos^(- 1)x),(cos^(- 1)z,cos^(- 1)x,cos^(- 1)y)] such that |A| = 0 , then maximum value of x + y + z is

Let a curve y = y (x) be given by the solution of differential equation cos ((1)/(2) cos ^(-1) (e ^(-x)) ) dx = sqrt ( e ^( 2x) - 1)dy If it intersects y – axis at y = –1, and the intersection point point of the curve with x – axis is (alpha, theta), then e ^(alpha) is equal to __________.

if y=e^(cos^(-1)x) then find dy/dx .

If y= cos ^(-1) ( e^(x)) , find ( dy )/(dx)

If sec^(-1)x=cos e c^(-1)y , then find the value of cos^(-1)(1/x)+cos^(-1)(1/y)