y=sqrt(((x-1)(x-2))/(x-3)(x-4)(x-5))

y=sqrt(((2x+3)^(5))/((3x-1)^(3)(5x-2))) Find dy/dx

Find the derivatives w.r.t. x : y=sqrt(((x-3)(x^(2)+4))/(3x^(2)+4x+5))

If y = sqrt(((x-3)(x^2+4))/((3x^2 + 4x + 5)) , then find dy/dx

If y=sqrt(((x-3)(x^(2)+4))/((3x^(2)+4x+5))) , find (dy)/(dx) .

Solve : (i) sqrt((x)/(x-3))+sqrt((x-3)/(x))=(5)/(2) (ii) ((2x-3)/(x-1))-4((x-1)/(2x-3))=3

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)

The value of f(x,y)=((4sqrt(x^(3)y)-4sqrt(x^(3)))/(sqrt(y)-sqrt(x))+(1+sqrt(xy))/(4sqrt(xy)))^(-2)(1+2sqrt((y)/(x))+(y)/(x))^((1)/(2)) when x=9,y=0.04

Find y ' , if (a) y=5x^(2//3)-3x^(5//2)+2x^(-3) (b) y=(a)/(3sqrt(x))^(2)-(b)/(x^(3)sqrt(x) (a,b constants )