Question

Differentiation using quotient rule: Can somebody please tell me how to solve this red arrow part, see the attached image file

Answer 1

8-12=-4, so you have -4x^2
That part is just algebra

Answer 2

No, I meant to say where we got that 8^4 +24x part

Answer 3

8x^3*x
from previous step

Answer 4

yes but how, can you please explain it ..

Answer 5

(x * y') - (x' * y) / (x)^2

Answer 6

Simplify this
\[ \frac{(x^3 + 3)8x - 4x^2 (3x^2)}{(x^3+2)^2}\]

Answer 7

(3x^3+8x-4x^2) / (x^3+2)^2

Answer 8

oh sorry, I didn't see the power signs are too small ..

(x^3+3 +8x) - (12x^2) / (x^3+3)^2

Answer 9

When you simplify it you will get the final answer shown below the red arrow.

Answer 10

yes, I am not good at simplifying. I almost forgot it.

Answer 11

your steps are incorrect!!
how can you be doing calculus ... ?? i think you should start with basic algebra

Answer 12

Let try basic algebra :
(x³+3) 8x = ...

Answer 13

can you please mention a link or tutorial where I can learn simplification and algebra. I don't think I am able to do derivative unless I learn some basic algebra.

Answer 14

Can distribute ( multiply) 8x into the parentheses ?

Answer 15

you?

Answer 16

8x^3+3 ?

Answer 17

How about: 8x * x³ = ..

Answer 18

24x^3 ?

Answer 19

Add exponents when you multiply

Answer 20

or it could be 8x and add powers? = 8x^4 ?

Answer 21

Don't get confused between exponent and the constant:

Answer 22

Yep, 8x^4 ( sigh !)

Answer 23

3* 8x = ?

Answer 24

24x , right?

Answer 25

Yep, now (x³+3) 8x = ...

Answer 26

8x^4 + 24x

Answer 27

and in the last part .. 4*3 = 12 ... then add exponents 12x^4

Answer 28

Great :)
4x² * 3x² =

Answer 29

Good job, now put them together!

Answer 30

Thank you so much @Chlorophyll .. Can you please give me a tutorial link where I can do exercises of simplifcations?

Answer 31

No more confused!

Answer 32

http://www.khanacademy.org/

Answer 33

thank you very much all of you. :) this community is really helpful.

Answer 34

http://www.regentsprep.org/regents/math/ALGEBRA/AO5/PracExp.htm

Answer 35

Hope you'll improve greatly at your next post :)