Question

1. (a) use the product rule with g=f to show that if f is differentiable, then
\[\frac{ d }{ dx }\left[ f(x) \right]^2= 2f(x)f ' (x)\]
(b) Use part (a) to differentiate y=(2+5x-x^3)^2.

Answer 1

Do you know the product rule? If so please state it.

Answer 2

(fg)' = f' g + f g'

Answer 3

Now replace all the gs with fs

Answer 4

(fg)' f' f +f f'

Answer 5

with equal b/w (fg)' and f'

Answer 6

And also that other g and we will pretend there is an equal sign there :)

Answer 7

(ff)' = f' f +f f'

Answer 8

(ff) '=ff' +ff'

Answer 9

there's a lot of fs :)

Answer 10

So you know x+x=2x so what is ff'+ff'

Answer 11

f '(2f) ?

Answer 12

You can say 2ff'

Answer 13

okay

Answer 14

I don't like using parenthesis sometimes in multiplication

Answer 15

Anyways any questions

Answer 16

how do you do b)?

Answer 17

Do you understand the rule you proved in a

Answer 18

kinda...

Answer 19

f=2+5x-x^3 So what is 2*f*f'

Answer 20

2(2+5x-x^3) (2+5x-x^3) '=?

Answer 21

ooohh.. so we sub in 2+5x-x^3 in the f and f'
okay, thank you!!!

Answer 22

Np

Answer 23

can you help me with another question if you don't mind?