[" 10."y=(x-1)(x-2)(x-3)],[" 11."sqrt((x^(2)+x+1)/(2))]

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

If y=(1)/(3)"log" (x+1)/(sqrt(x^(2)-x+1))+(1)/(sqrt(3))"tan"^(-1)(2x-1)/(sqrt(3)) , show that, (dy)/(dx)=(1)/(x^(3)+1)

Equation of a line which is tangent to both the curve y=x^(2)+1 and y=x^(2) is y=sqrt(2)x+(1)/(2) (b) y=sqrt(2)x-(1)/(2)y=-sqrt(2)x+(1)/(2)(d)y=-sqrt(2)x-(1)/(2)

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

y=(sqrt(x)+(1)/(sqrt(x)))(1+x+x^(2))

The expression (sqrt(x^(3)-1)+x^(2))^(11)-(sqrt(x^(3)-1)-x^(2))^(11) is a polynomial of degree

Simplify : (a) sqrt(y+sqrt(2xy-x^(2))) + sqrt(y-sqrt(2xy-x^(2))) (b) (x+sqrt(x^2-1))/(x-sqrt(x^(2)-1)) -(x-sqrt(x^(2)-1))/(x+sqrt(x^(2)-1))

If y=(sinh^(-1)x)/(sqrt(1+x^(2))) then (1+x^(2))y_(2)+3xy_(1)=

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

Which of the following expressions are polynomials ? In case of a polynomial , write its degree. (i) x^(5)-2x^(3)+x+sqrt(3) (ii) y^(3)+sqrt(3)y (iii) t^(2)-(2)/(5)t+sqrt(5) (iv) x^(100)-1 (v) (1)/(sqrt(2))x^(2)-sqrt(2)x+2 (vi) x^(-2)+2x^(-1)+3 (vii) 1 (viii) (-3)/(5) (ix) (x^(2))/(2)-(2)/(x^(2)) (x) root(3)(2)x^(2)-8 (xi) (1)/(2x^(2)) (xii) (1)/(sqrt(5))x^(1//2)+1 (xiii) (3)/(5)x^(2)-(7)/(3)x+9 (xiv) x^(4)-x^(3//2)+x-3 (xv) 2x^(3)+3x^(2)+sqrt(x)-1