Question

find the derivative of F(x)=integral from x to 4 of (sin(t^(4)))dt

Answer 1

\[\int_x^4sin(t^4)dt?\]

Answer 2

well what is

\[\frac{d}{dx}\int\]

Answer 3

yeah that^

Answer 4

use the fundamental theorem of calculus

Answer 5

\[f(x)=\frac{d}{dx}F(x)\]

Answer 6

\[F(x)=\int_x^4sin(t^4)dt\]

Answer 7

Okay, gimme a sec.

Answer 8

I find F(x) very vague for this i think it should be

\[F(x)=\int_x^4 sin(t^4)=F(4)-F(x)
\]
\[\frac{d}{dx}(F(4)-F(x))=0-F'(x)(1)=-f(x)\]

Answer 9

the one inside is F(t) for x whereas the outside is just F(x)

Answer 10

so it ends up being \[f(t)=sin(t^4)\]
\[f(x)=f(t)|_0^x\]
you can say i guess

Answer 11

\[-sin(x^4)\]

Answer 12

make sense?