y=sqrt((1+sin x)/(cos x))" and "y=sqrt((1-sin x)/(cos x))

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

y=sqrt(sin +cos x+sqrt(sinx+ cos x +sqrt(sin x +cos x +....oo))) then find dy/dx

y=sqrt(sin +cos x+sqrt(sinx+ cos x +sqrt(sin x +cos x +....oo))) " then find " dy/dx

If x= sqrt ( a^( sin^(-1) t) ) and y= sqrt ( a^( cos^(-1) t) ), then show that dy/dx = -(y/x)

Differentiate y with respect to x, where [y= tan^-1 { sqrt(1+sin x) + sqrt(1- sin x)} / {sqrt (1+ sin x) - sqrt(1- sin x)}]

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

If x=sqrt(a^(sin^(-1)t)" and "y=sqrt(a^(cos^(-1)t) show that (dy)/(dx)=-(y)/(x) .

sqrt(cos 2x) + sqrt(1 + sin 2x) = 2sqrt(sin x + cos x) if

Applying logrithmic differentiation find the derivatives of the following functions (a) y=(cos x)^(sin x) (b) y=((3 sqrt(sin 3x))/(1-sin 3x)) (c ) y=sqrt(x-1)/((3sqrt(x+2))^(2)(sqrt(x+3))^(3))