Question

in the problem
f(x)=x^n where n=1,2,3....
what is (d/dx)x^n?
you get ((x+delta(x))^n -x^n)/(delta(x))
where does -x^n come from if the difference quotient is:
(f(x-delta(x))-f(x))/(delta(x)) ?

thanks

Answer 1

\[((x_0+\Delta x )^{n}-x^{n}_0)/\Delta x\]

Answer 2

The difference quotient is \[(f(x+\Delta x) - f(x))/\Delta x\]so given that f(x)=x^n, the -x^n value in your equation if the substitution of f(x) into the difference quotient.

Answer 3

thanks Xavier