(x-x_(0))(x-b)quad " (ii) "(ax^(1)+b)^(2)quad " (iii) "(x-a)/(x-b)

For some constants a and b,find the derivative of (i) (x-a)*(x-b)( ii) (ax^(2)+b)^(2) (iii) (x-a)/(x-b)

For some constants a and b, find the derivative of : (i) (x-a)(x-b) (ii) (ax^(2)+b)^(2) (iii) (X-a)/(x-b)

For some constant a and b, find the derivative of i. (x-a)(x- b) ii. (ax^(2)+b)^(2) iii. (x-a)/(x-b)

For some constants a and b, find the derivative of(i) (x - a) *(x-b) (ii) (a x^2+b)^2 (iii) (x-a)/(x-b)

Factorise the following expressions : (i) ax-ay+bx-by " " (ii) x^(2)-x-ax+a " " (iii) x^(4)+x^(3)+x^(2)+x (iv) 16(a+b)^(2)-4a-4b " " (v) x^(2)+(1)/(x^(2))+2-3x-(3)/(x) " " (vi) x^(2)-((a)/(b)+(b)/(a))x+1 (vii) x^(2)+(a-(1)/(a))x-1 " " (viii)ab(x^(2)+y^(2)+xy(a^(2)+b^(2)) " "(ix) (ax+by)^(2)+(bx-ay)^(2)

Prove that. (i) sqrt(x^(-1) y) .sqrt(y^(-1) z) . Sqrt(z^(-1) x) = 1 (ii) ((1)/(x^(a-b)))^((1)/(a-c)).((1)/(x^(b-c))).((1)/(x^(c-b)))^((1)/(c-b))= 1 (iii) (x^(a(b-c)))/(x^(b(a-c))) div ((x^(b))/(x^(a))) (iv) ((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))

If f((ax+b)/(x-a))=x, then f^(-1)(x)= (a) x (b) (bx+a)/(x-b)( c) f(x)

If a is a constant prove that (i) var(a)=0 (ii) var (aX)=a^(2)var(X) (iii) Var(ax+b)=a^(2)var(X)

If y=(1)/(sqrt(a^(2)-b^(2)))cos^(-1)((a cos x+b)/(a+b cos x)), then (d^(2)y)/(dx^(2))=(i)(b sin x)/((a+b cos x)^(2))( ii) -(b sin x)/((a+b cos x)^(2))( iii) (b cos x)/((a+b cos x)^(2))( iii) -(b cos x)/((a+b cos x)^(2))