If `f(x) = ax^n`, prove that `a = (f'(1))/(n)`.

If f(x) = alpha x^n , prove that alpha= (f'(1))/n .

If f (x) = (a-x^n)^(1//n) prove that f(f(x)) = x

if f(x) = x^n then the value of f(1) - (f'(1))/(1!) + (f''(1))/(2!) + ---+((-1)^n f''^--n times (1))/(n!)

If f(x) =x+1/x , prove that : [f(x)]^3 = f(x^3)+3f (1/x) .

If y= f(x) =(ax-b)/(bx-a) , prove that f(y) =x.

If f(x)= (1 + x)^n then the value of f(0) + f'(0) + (f''(0))/(2!) + .... + (f^n(0))/(n!) is

If f (x) = log_e ((1+x)/(1-x)) , prove that: f (x) +f (y)= f ((x+y)/(1+xy)) .

If y = |[f(x),g(x),h(x)],[1,m,n],[a,b,c]| , prove that dy/dx = |[f'(x),g'(x),h'(x)],[l,m,n],[a,b,c]|

Let f(x+y)=f(x)+f(y)+2x y-1 for all real xa n dy and f(x) be a differentiable function. If f^(prime)(0)=cosalpha, the prove that f(x)>0AAx in Rdot

If f(x)=ax+b and the equation f(x)=f^(-1)(x) be satisfied by every real value of x, then