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

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

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

Find (dy)/(dx) , when : If y=((cos x - sin x))/((cos x + sin x)) , prove that (dy)/(dx)+y^(2)+1=0 .

If y=sin^(-1) x+cos^(-1) x,"then "dy/dx=

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

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

If y = sin(2 cos^(-1)x) , then prove that (1 - x^2)(d^2y)/(dx) -x dy/dx + 4y = 0

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

x = sqrt(a^(sin^(-1)t)), y=sqrt(a^(cos^(-1)t)) , Prove that: (dy)/(dx) = -y/x

If y=tan^(-1)((sin x + cos x)/(cos x - sin x)) , then (dy)/(dx) is equal to