Question

Find f'(x).

Answer 1

y=f'(x)=(3x+2)(4x-5)

Answer 2

I've gotten this far.

y=f'(x)=(3x+2)(4x-5)' + (4x-5)(3x+2)'

Answer 3

I know this is next but, I'm not sure how to get the '?'s
= (3x+2) (?) + (4x-5) (?)

Answer 4

(4x-5)'=?
(3x+2)'=?

Answer 5

you that dx/dx=1
and use the constant multiple rule
and also the constant rule

Answer 6

also I would call it y' not y

Answer 7

\[\frac{d}{dx}(4x-5)= \frac{d}{dx}(4x)-\frac{d}{dx}(5) \text{ by difference rule } \\\]
now apply the other rules I have mentioned

Answer 8

I am so sorry, freckles. I don't know the constant multiple rule. I also don't fully understand the equation you have up.

Answer 9

you never seen d/dx ?

Answer 10

my teacher taught us to change it to f'(x).

Answer 11

to make it easier.

Answer 12

Again, I apologize.

Answer 13

d/dx means find the derivative with respect to x

Answer 14

the constant multiple rule means you can bring the constant multiple outside the differentiating operator

Answer 15

\[\frac{d}{dx}(ax+b)=\frac{d}{dx}(ax)+\frac{d}{dx }b \text{ by \sum rule } \\ =a \frac{d}{dx}x+\frac{d}{dx} b \text{ by constant multiple rule } \\ =a \frac{dx}{dx}+0 \text{ by constant rule } \\ =a(1) \text{ since } \frac{dx}{dx}=1\]
so
\[\frac{d}{dx}(ax+b)=a\]
so you never seen these rules before?

Answer 16

I have seen this except, in the f'(x) format.
What you have up does make sense to me. I am looking at my textbook and I did apparently 'learn' constant rule and multiple constant property.

Answer 17

So, I can use (4x-5)' and (3x+2) and input that iinto the equation above and I will be given my answer to help with the rest of the problem?

Answer 18

yes

Answer 19

Thank you so much, freckles.
I'm slow when it comes to math so I'm sorry if I'm frustrating to deal with.
I am working out the problem right now.

Answer 20

I didn't think you were frustrating at all

Answer 21

Thanks. :]
Okay, so I got 22x-14 as the answer. Here is my work:

and