If `f(x)=alphax^n ,` prove that `alpha=(f^(prime)(1))/n` .

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

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

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

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

If g is the inverse of f and f'(x)=1/(1+x^n) , prove that g^(prime)(x)=1+(g(x))^n

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

Let f(x)a n dg(x) be two differentiable functions in R a n d f(2)=8,g(2)=0,f(4)=10 ,a n dg(4)=8. Then prove that g^(prime)(x)=4f^(prime)(x) for at least one x in (2,4)dot

Let f(x)a n dg(x) be two differentiable functions in R a n d f(2)=8,g(2)=0,f(4)=10 ,a n dg(4)=8. Then prove that g^(prime)(x)=4f^(prime)(x) for at least one x in (2,4)dot

If f(x)=(1+x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+(f^(''')(0))/(3!)+......(f^n(0))/(n !)dot

If f(x)=(1+x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+(f^(''')(0))/(3!)+......(f^n(0))/(n !)dot