Question

Find F(x+h)-F(x)/h
F(x)=x^n

Answer 1

\[\frac{F(x+h)-F(x)}{h}=\frac{(x+h)^n-x^n}{h}\]
now how would you like to expand ?

Answer 2

you will get
\[\frac{x^n+nx^{n-1}h+\dbinom{n}{2}x^{n-2}h^2+...-x^n}{h}\]
\[=\frac{nx^{n-1}h+\text{ stuff with higher powers of }h}{h}\]
so when you cancel the h you will have
\[nx^{n-1}+\text{ terms that include } h\]and when you take the limit as h goes to zero you will get
\[nx^{n-1}\]