`y=sin^(-1)((5x+12sqrt(1-x^2))/(13))`

Find (dy)/(dx) in the following : y= sin^(-1) (2x sqrt(1-x^(2))), (1)/(sqrt(2)) lt x lt (1)/(sqrt(2)) .

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

Evaluate: int_0^(1/(sqrt(2)))(sin^(-1)x)/((1-x^2)sqrt(1-x^2))dx

y = sin^(-1)(x/sqrt(1+x^2)) + cos^(-1)(1/sqrt(1+x^2))

Prove that tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x)/(sqrt(1+x^(2))*sqrt(1+y^(2))))

Find (dy)/(dx)," if "y= sin^(-1)x +sin^(-1)sqrt(1-x^(2)), 0 lt x lt 1 .

If x in[-1,(-1)/(sqrt(2))] , then the inverse of the function f(x)=sin^(-1)(2x sqrt(1-x^(2))) is given by

Integrate the following functions w.r.t x. (sin^(-1)x)^(5)/(sqrt(1-x^2))

Integrate the functions (sin^(-1)x)/(sqrt(1-x^(2)))