derritatvies question

[dire forge]

idk what to do for the rest of of these questions

[amber gust]

Do you know about the product and chain rule for derivates?

[dire forge]

ye

[amber gust]

Do you think you can apply those to some of these?

[dire forge]

wow i can apply chain rule to the first part and apply the product rule to the third one and last one right?

wait no not the last one

[amber gust]

For the 4th you need the sum rule, that's the easiest one

[dire forge]

yea but i tried doing 1-6

and 2-9

for the fourth one

[amber gust]

2-9 should be it

[dire forge]

i tried -6

but it didnt work

[amber gust]

Because 2-9 = -7?

[dire forge]

ohhhhhh

my bad cuh

[amber gust]

🙂

[dire forge]

wow so then for the third one i use product rule?

[amber gust]

Correct

[dire forge]

hmm for the first one chain rule works like
f'(x)*f(x)-f'(x). which should be 2(1)-2?

im assuming its asking for the f' and f values from 1

oh wait

i dont do -f'

my bad

thanks i got it now

[amber gust]

No that is incorrect

[dire forge]

yea it was (f'(x)*f(x) * f'(x) right?

[amber gust]

It's f'(f(x))f'(x)

[dire forge]

oh what the

yea thats what i meant to type

[amber gust]

$\frac{d}{dx} f(u(x)) = \frac{d}{du}f(u)\frac{d}{dx}u(x)$

[shut mauve]

WanderingLethe

[amber gust]

Do you know this notation @dire forge ?

Have to say this is also pretty elegant

$(f\circ g)'=(f'\circ g)\cdot g'$

[shut mauve]

WanderingLethe

[amber gust]

In contrast with, the product rule:

$(f \cdot g)' = f' \cdot g + f \cdot g'$

[shut mauve]

WanderingLethe

[dire forge]

wow im going to write these down

we just learnt this today so im going tosome more practice on these questions

[amber gust]

The first two are just different notations of the chain rule

How have you learned them?

The d/dx is the Leibniz notation, meaning take the derivate with respect to x.