Question

find the derivative of the function g(x)=int_{a}^{x}f(t)dt=f(x)

Answer 1

if i remember it right:

f(x)x'- f(a)a'

Answer 2

\[g(x)=\int_{a}^{x}f(t)\ dt\]
\[G(x)=F(x)-F(a)\]
\[[G(x)=F(x)-F(a)]'\]
\[g(x)=f(x)x' - f(a)a'\]

Answer 3

im assuming there that a and x are functions of x, which might be a bad idea

Answer 4

if a is a constant don't we get a'=0
?
we do assume it's a constant, right?

Answer 5

i never assume letters to be constants unless told otherwise ;)

Answer 6

fair enough, let the questioner correct us if needed