Find the derivative of `x^n+ax^(n-1)+a^(2)x^(n-2)+..........+a^(n-1)x+ a^(n)` for some fixed real number a.

Find the derivative of x^n + a^n for some fixed real number a .

Find the derivatives of the following : x/sin^n x .

Find the derivative of (x^n-a^n)/(x-a) for some constant a.

Differentiate |x|+a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)+...+a_(n-1)x+a_(n)

Find the derivatives of the following function : f(x) =(ax + b)^n .

Find value of (x+(1)/(x))^(3)+(x^(2)+(1)/(x^(2)))^(3)+"........"+(x^(n)+(1)/(x^(n)))^(3) .

The coefficient of x^r [0lt=rlt=(n-1)] in the expansion of (x+3)^(n-1)+(x+3)^(n-2)(x+2)+(x+3)^(n-3)(x+2)^2+.... +(x+2)^(n-1) is a.^n C_r(3^r-2^n) b.^n C_r(3^(n-r)-2^(n-r)) c. ^n C_r(3^r+2^(n-r)) d. none of these

In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N ,