Question

derivative s

Answer 1

how would i start off

Answer 2

I mean to have ds not dx

Answer 3

i know i use the chain rule but everytime i do it it's not the same answer my teacher got. She showed us in class but i still can't get it

Answer 4

\[\frac{d}{dx}( \int\limits_{a(x)}^{b(x)} f(s) ds) \\ \text{ Let } F'=f \\ \text{ That is \let } F \text{ be the antiderivative of } f \\ \frac{d}{dx} (F(s)|_{a(x)}^{b(x)} ) =\frac{d}{dx}(F(b(x))-F(a(x))) \\ \text{ then use difference rule } \\ =\frac{d}{dx}(F(b(x))-\frac{d}{dx}(F(a(x)) \\ \\ \text{ then use chain rule } \\ =b'(x) \cdot F'(b(x))-a'(x) \cdot F'(a(x)) \\ \text{ recall } F'=f \\ \text{ so we have} \\ =b'(x) f(b(x))-a'(x) f(a(x))\]

Answer 5

well first of all you do know f(s)=s^2/(4+5s^4) right?

Answer 6

yes i got that

Answer 7

i'll try to draw our my work

Answer 8

and you also notice b(x)=1 so b'(x)=0
and if a(x)=sqrt(x) then a'(x)=?

Answer 9

ummm can u use the example to show me? I'm not sure with the a and b stuff. Like i need to see real numbers ><

Answer 10

well a(x) is your lower limit
b(x) is your upper limit

Answer 11

like in your problem a(x) is sqrt(x)
and b(x) is 1

Answer 12

can you tell me what a'(x) is given that a(x)=sqrt(x)?

Answer 13

I have to go
peace

Answer 14

im sorry im lost

Answer 15

i know i use the chain rule but it just won't work out

Answer 16

Did you get it now?

Answer 17

nope

Answer 18

It's been 6 hours and you still haven't got it?

Answer 19

it's just a problem i want to learn to do for my self lol. if i don't get it it's ok. it's not hw or test material. It was i my notes and i wanted to understand it and that's it....