>>12836143Just use the binomial formula
(x+h)^n= x^n + nhx^(n-1) + n(n-1)/2 h^2 x^(n-2) + ...
The term linear in h is nx^(n-1).
Actually the binomial formula is overkill. We're looking for the term linear in h in (x+h)^n=(x+h)....(x+h) n times.
The way you multiply it is you pick one term from each term in the product. You need to pick exactly one h and exactly n-1 x's. Since h can come form any of the terms, there is factor of n. So the term linear in h is nhx^(n-1).
Another way is product rule
d/dx x^n = d/dx x*x*x*x..*x = 1*x...*x + x*1*x....*x + x*x*1*...*x + ..+ x*....*x*1 = nx^(n-1).
