If `y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !),` show that `(dy)/(dx)-y+(x^n)/(n !)=0.`

If y=1+x+(x^2)/(2!)+(x^3)/(3!)+...+(x^n)/(n !),t h e n(dy)/(dx) is equal to (a) y (b) y+(x^n)/(n !) (c) y-(x^n)/(n !) (d) y-1-(x^n)/(n !)

Statement 1: The coefficient of x^n is (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !))^3 is (3^n)/(n !) Statement 2: The coefficient of x^n ine^(3x)i s(3^n)/(n !)

If y=(1+x)(1+x^2)(1+x^4)......(1+x^(2n)), then find (dy)/(dx)a tx=0.

If 2 cos alpha = x + (1)/(x) and 2 cos beta = y + (1)/(y) , show that (x^(m))/(y^(n))- (y^(n))/(x^(m))= 2i sin (m alpha - n beta)

If x^m y^n=(x+y)^(m+n),prove (dy)/(dx)=y/xdot

Given (x_(1) + iy_(1)) (x_(2) + iy_(2))…(x_(n) + iy_(n)) = a + ib, show that (x_(1)^(2)+y_(1)^(2))(x_(2)^(2) + y_(2)^(2))(x_(3)^(2) + y_(3)^(2))…(x_(n)^(2) + y_(n)^(2)) = a^(2) + b^(2)

Let y=e^(x sin x^3)+(t a n x)^x Find (dy)/(dx)

If 2 cos alpha = x + (1)/(x) and 2 cos beta = y + (1)/(y) , show that x^(m) y^(n) + (1)/(x^(m)y^(n)) = 2 cos (m alpha + n beta)

If S_(n)=(x+y)+(x^(2)+xy+y^(2))+(x^(3)+x^(2)y+y^(2)x+y^(3))+…n terms then prove that (x-y)S_(n)=[(x^(2)(x^(n)-1))/(x-1)-(y^(2)y^(n)-1)/(y-1)] .

If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b) n(n+1)y (c) n y (d) n^2y