# Thread: My derirative answer for function f(x) = (3x + 2)*(2x^2 - 1)

1. ## My derirative answer for function f(x) = (3x + 2)*(2x^2 - 1)

9. For the function f (x) = (3x + 2)(2x2 - 1):

a. Find the derivative using the Product Rule.
b. Expand and simplify the function; then use the Sum and Difference Rule to find the derivative.
c. What do you conclude from the results in parts (a) and (b)?

Hey,

First I'd like to apologize to Subhotosh Khan and stapel - I unfortunately got your messages late and realized I asked my question without providing the original maths problem. Therefore I am providing it again. I have worked out most of this(if it's correct) so don't worry.

So question a is asking for the derivative which is 18x2+8x3

so question b is asking me to EXPAND and SIMPLIFY the FUNCTION--the original function that is. The answer to this is 6x3−3x+4x2...then it asks to use the sum rule to find the derivative. This equals 18x^2−3+8x which equals back to the derivative

And question c is asking what I can really conclude about this. Nothing really pops up in my brain for this. Could you guys guide me on the right track?

2. Originally Posted by Alexmcom
9. For the function f (x) = (3x + 2)(2x2 - 1):

a. Find the derivative using the Product Rule.
b. Expand and simplify the function; then use the Sum and Difference Rule to find the derivative.
c. What do you conclude from the results in parts (a) and (b)?

Hey,

First I'd like to apologize to Subhotosh Khan and stapel - I unfortunately got your messages late and realized I asked my question without providing the original maths problem. Therefore I am providing it again. I have worked out most of this(if it's correct) so don't worry.

So question a is asking for the derivative which is 18x2+8x3

so question b is asking me to EXPAND and SIMPLIFY the FUNCTION--the original function that is. The answer to this is 6x3−3x+4x2...then it asks to use the sum rule to find the derivative. This equals 18x^2−3+8x which equals back to the derivative

And question c is asking what I can really conclude about this. Nothing really pops up in my brain for this. Could you guys guide me on the right track?
Did you use the product rule for part (a)? Given your answer, I would think not...

3. Originally Posted by Alexmcom
9. For the function f (x) = (3x + 2)(2x2 - 1):

a. Find the derivative using the Product Rule.
b. Expand and simplify the function; then use the Sum and Difference Rule to find the derivative.
c. What do you conclude from the results in parts (a) and (b)?

So question a is asking for the derivative which is 18x2+8x3
Actually, this part of the question is asking you to show how you got the derivative; in particular, to show your use of the specified method. I'm not seeing this here.

Originally Posted by Alexmcom
so question b is asking me to EXPAND and SIMPLIFY the FUNCTION--the original function that is. The answer to this is 6x3−3x+4x2...then it asks to use the sum rule to find the derivative. This equals 18x^2−3+8x which equals back to the derivative
This part again asks you to show your work. I'm not seeing this here.

Originally Posted by Alexmcom
And question c is asking what I can really conclude about this. Nothing really pops up in my brain for this. Could you guys guide me on the right track?
Since you haven't shown your work, there is little for you to compare, contrast, etc, so there is little that can be "concluded". If you had work that could be examined, one might wonder if they're maybe looking for some thoughts on the results, regardless of the method used.

4. Originally Posted by stapel
Actually, this part of the question is asking you to show how you got the derivative; in particular, to show your use of the specified method. I'm not seeing this here.

This part again asks you to show your work. I'm not seeing this here.

Since you haven't shown your work, there is little for you to compare, contrast, etc, so there is little that can be "concluded". If you had work that could be examined, one might wonder if they're maybe looking for some thoughts on the results, regardless of the method used.

ahhh Sorry I didn't think I would have to show but here u go.

for question a) Using the product rule: f'(x)g(x)+f(x)g'(x)

(3x+2)(2x^2-1)

fx=3x+2
gx=2x^2-1
f'(x)=3
g'x=4x

(3)(2x^2-1)+(3x+2)(4x)

6x^2-3+12x^2+8

add them together and its 18x^2+8x-3

now for question B

(3x+2)(2x21)

expand and simplify so its 6x^3-3x+4x^2-2 and now we use sum and difference rule on our expanded equation. so 6(3)^2-3(1)+4(2x)-2=18x^2-3+8x

5. Originally Posted by Prove It
Did you use the product rule for part (a)? Given your answer, I would think not...

Yes I used product rule f'(x)g(x)+f(x)g'(x)

6. Originally Posted by Alexmcom
ahhh Sorry I didn't think I would have to show but here u go.

for question a) Using the product rule: f'(x)g(x)+f(x)g'(x)

(3x+2)(2x^2-1)

fx=3x+2
gx=2x^2-1
f'(x)=3
g'x=4x

(3)(2x^2-1)+(3x+2)(4x)

6x^2-3+12x^2+8$\ \ \ \ \ \ \$ The last term is incorrect. Maybe it was due to a typo.

add them together and its 18x^2+8x-3$\ \ \ \ \ \ \$You have the result corrected by this step.

now for question B

(3x+2)(2x21) $\ \ \ \ \ \$ Make that (3x + 2)(2x^2 - 1)

expand and simplify so its 6x^3-3x+4x^2-2 and now we use sum and difference rule on our expanded equation. so 6(3)^2-3(1)+4(2x)-2=18x^2-3+8x $\ \ \ \ \ \ \$ Incorrect. See ** below.
**

(3x + 2)(2x^2 - 1) =

6x^3 - 3x + 4x^2 - 2

There are no like terms to combine, but write the terms in descending order of degree:

6x^3 + 4x^2 - 3x - 2

Take the derivative in a similar fashion to how you did it, but note the differences:

6(3x^2) + 4(2x) - 3(1) - 0 =

18x^2 + 8x - 3 $\ \ \ \ \ \ \ \$ That is the answer for part b.

7. Originally Posted by lookagain
**

(3x + 2)(2x^2 - 1) =

6x^3 - 3x + 4x^2 - 2

There are no like terms to combine, but write the terms in descending order of degree:

6x^3 + 4x^2 - 3x - 2

Take the derivative in a similar fashion to how you did it, but note the differences:

6(3x^2) + 4(2x) - 3(1) - 0 =

18x^2 + 8x - 3 $\ \ \ \ \ \ \ \$ That is the answer for part b.

Yes you are correct...that was indeed a typo--I type quite fast.

Now I am just stuck on question C.

I'm trying to do research to figure out if there is a relation between the different methods it asked me to use.

8. Originally Posted by Alexmcom
I'm trying to do research to figure out if there is a relation between the different methods it asked me to use.
What is the difference in the results? (Hint: None.) So what does this suggest about the two different methods?

9. Originally Posted by stapel
What is the difference in the results? (Hint: None.) So what does this suggest about the two different methods?

I would say since there are no difference in the results, I could conclude that the two methods used are simply other ways of finding the derivative.

I can't really say much but I know there's more to it.

10. Originally Posted by Alexmcom
I would say since there are no difference in the results, I could conclude that the two methods used are simply other ways of finding the derivative.

I can't really say much but I know there's more to it.
Maybe there isn't "more to it". When you've got two equally-legitimate ways to approach an exercise, as long as each step in your process is valid, the approaches should all lead to the same final result. Maybe it's as simple as that!

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