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

a) Find (dy)/(dx) where (i) y=x^(log x)+(log x)^(x) (ii) y=sin^(-1)((x)/(sqrt(a^(2)+x^(2))))

Find (dy)/(dx) where (i) y=x^(log x)+(log x)^(x) (ii) y=sin^(-1)((x)/(sqrt(a^(2)+x^(2))))

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

If y=sin^(-1)((2sqrt(x^(2)-1))/(x^(2))) , then find (dy)/(dx) .

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

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

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

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

If y=(sin^(-1)x)/(sqrt(1-x^(2))), then ((1-x^(2))dy)/(dx) is equal to x+y (b) 1+xy1-xy(d)xy-2

If y=(x sin^(-1)x)/(sqrt(1-x^(2)))+log sqrt(1-x^(2)), then prove that (dy)/(dx)=(sin^(-1)x)/((1-x^(2))^((3)/(2)))