please help! having issue with exponent part of problem. I come to 16x^4 but I think it should be 16x^3.i also have complications with finding the domains.

Question

find the derivative of the function using the definition of derivative.
f(x)=4x^4
f'(x)=?
State the domain of the function.
state the domain of its derivative.

Answer 1

f(x+h) = 4(x+h)^4 = 4(x^4+4x^3h+6x^2h^2+4xh^3+h^4

f(x+h)-f(x) = 4(4x^3h+6x^2h^2+4xh^3+h^4)

(f(x+h)-f(x))/h = 4(4x^3+6x^2h+4xh^2+h^3)

now take the limit as h->0 and you have 16x^3

the domain of any polynomial is all real numbers