" vi) If "y=e^(a sin^(-1)x)," then show that "(dy)/(dx)=(ay)/(sqrt(1-x^(2)))

If y = e^(asin^(-1)x) then prove that (dy)/(dx) = (ay)/(sqrt(1 - x^2))

If y=e^(a sin^(-1)x) then prove that dy/dx=(ay)/(sqrt(1-x^(2)) .

If y=sin(2sin^(-1)x) , show that: (dy)/(dx)=2sqrt((1-y^(2))/(1-x^(2))) .

If y = f(x) and x = g(y), where g is the inverse of f, i.e., g = f^(-1) and if (dy)/(dx) and (dx)/(dy) both exist and (dx)/(dy) ne 0 , show that (dy)/(dx) = (1)/((dx//dy)) . Hence, (1) find (d)/(dx) (tan^(-1)x) (2) If y=sin^(-1)x, -1lexle1, -(pi)/(2)leyle(pi)/(2) , then show that (dy)/(dx)=(1)/(sqrt(1-x^(2))) where |x| lt 1 .

If sin y=x sin(a+y), then show that: (dy)/(dx)=(sin a)/(1-2x cos a+x^(2))

If y=sin^(-1) x , show that ((dy)/(dx))_(x=0)=1 .

If e^(y)(x+1)=1, show that (dy)/(dx)=-e^(y)

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

If y = sin^(-1){(5x+12sqrt(1-x^2))/13} then show that (dy)/(dx) = 1/sqrt(1-x^2)