y=x^(3)sqrt((x^(2)+4)/(x^(2)+3))

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))) , find (dy)/(dx) .

Show that: (x^((2)/(3))sqrt(y^(-2)))/(y^(2)sqrt(x^(-2)))times(y^(2)sqrt(x^(-2)))/(sqrt(x^((4)/(3))))=(1)/(y)

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 )

Rationalise the denominator: (a) (1)/(root(3)(3) + root(3)(2)) , (b) (2)/(sqrt5 + sqrt3 + sqrt2) , (c) (x^(2))/(sqrt(x^(2) + y^(2)) - y) , (d) (1)/(sqrt6 + sqrt5 - sqrt11) (e) (sqrt(x + 2y) - sqrt(x -2y))/(sqrt(x + 2y) + sqrt(x - 2y)) , (f) (sqrt10 + sqrt5 - sqrt3)/(sqrt10 - sqrt5 + sqrt3)

lim_(x to oo ) (sqrt(3x^(2)-1)-sqrt(2x^(2)-3))/(4x+3)

lim_(x to oo ) (sqrt(3x^(2)-1)-sqrt(2x^(2)-3))/(4x+3)

Differentiate y = (x^(3/4) sqrt(x^2 + 1))/((3x+2)^5) .