" (iii) "sin^(-1)((a+b cos x)/(b+a cos x))

Differentiate the following functions with respect to x:log(sec x+tan x)( ii) e^(x sin x)sin^(-1)(x^(3))(iv)sin^(-1)((a+b cos x)/(b+a cos x)),b>a

Differentiate sin^(-1)((a+b cos x)/(b+a cos x)),b>a with respect to x:

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)

(b) tan^(-1)((1-cos x)/(sin x))

If y=(1)/(sqrt(a^(2)-b^(2)))cos^(-1)((a cos x+b)/(a+b cos x)), then (d^(2)y)/(dx^(2))=(i)(b sin x)/((a+b cos x)^(2))( ii) -(b sin x)/((a+b cos x)^(2))( iii) (b cos x)/((a+b cos x)^(2))( iii) -(b cos x)/((a+b cos x)^(2))

If y= tan^(-1)((a cos x-b sin x)/(b cos x+a sin x))" show that, " (dy)/(dx)= -1 .

y=tan^(-1)((a cos x-b sin x)/(b cos x+a sin x)), where -(pi)/(2) -1

Find (dy)/(dx) in the following: y= tan^(-1) ((a cos x- b sin x)/(b cos x + a sin x))