Calculate the limit of the fraction (f(x)-f(1))/(x-1) if f(x)=x^300+x+1, x-->1

We notice that if we'll calculate the limit of the given
ratio, we'll calculate the first derivative of the given function, for x =
1.

lim (f(x)-f(1))/(x-1) =
f'(1)

For this reason, we'll calculate first the derivative
of the function:

f'(x) = 300x +
1

Now, to evaluate f'(1), we'll substitute x by 1 in the
expression of derivative:

f'(1) = 300*1 +
1

f'(1) = 301

So, it is no
need to struggle calculating the limit of the ratio, when we can do an easier
way:

lim [(f(x)-f(1))/(x-1)] = 301 for
x-> 1