If `y=sqrt((a-x)(x-b))-(a-b)tan^-1sqrt((a-x)/(x-b))`,show that `dy/dx=sqrt((a-x)/(x-b))`

If y=sqrt((a-x)(x-b))- (a-b)tan^(-1)sqrt((a-x)/(x-b)) then (dy)/(dx) is equals to

(dy)/(dx)=sqrt(y-x)

If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/((sqrt(a-x)+sqrt(x-b)) ,then (dy)/(dx) wherever it is defined is (a) (x+(a+b))/(sqrt((a-x)(x-b))) (b) (2x-a-b)/(2sqrt(a-x)sqrt(x-b)) (c) -((a+b))/(2sqrt((a-x)(x-b))) (d) (2x+(a+b))/(2sqrt((a-x)(x-b)))

int_(a)^(b)sqrt((x-a)/(x-b))dx

If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y) ,show that dy/dx=sqrt((1-y^2)/(1-x^2))

(dy)/(dx)=sqrt(x+y+1)

If y = sqrt(x/(a))-sqrt(a/(x)) show that 2xy (dy)/(dx)=(x)/(a)-(a)/(x)

y=tan^(-1) ((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)) show that dy/dx=1/(2sqrt(1-x^2))

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

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