# Thread: differentiate and simplify #5

1. ## differentiate and simplify #5

Can someone please check my answers below for accurateness? The instructions are: Differentiate and simplify.

1) y=(2x^2+3x-1)(3x^2-5x-3)
y'=(4x+3)(3x^2-5x-3)+(2x^2+3x-1)(6x-5)

2) y=(5x^2+3x-1)(3x^2-5x-3)
y'=(10x+3)(4x^2-3)+(5x^2+3x-1)(8x)

3)y=6x^3-7x^2+5x-7+x^(5/3)-7/(x^3)
y'=18x^2-14x+5+5x^(2/3)+21/(x^4)

4) y=[5x^4-3x^3+6x^2-5x+7-x^(3/2)]/x^2
y'=10x-3+5/(x^2)-14/(x^3)+1/(2((sqrt)x)^3)

5) y=(5x^2-3x+7)(3x^2+7x-2)(6x^2+4x-5)
y'=(10x-3)(3x^2+7x-2)(6x^2+4x-5)+(5x^2-3x+7)(6x+7)(6x^2+4x-5)+(5x^2-3x+7)(3x^2+7x-2)(12x+4)

6) y=(7x^3-5x^2+6x-3)^12
y'=12(21x^2-10x+6)(7x^3-5x^2+6x-3)^11

7) y=(4x^2+3)^5(2x^2-1)^4
y'=[8x(4x^2+3)^4(2x^2-1)^3][5(2x^2-1)+2(4x^2+3)]

8) y=(4x^2+3x-5)^(4/5)
y'=[4(8x+3)]/[5(4x^2+3x-5)^(1/5)]

O.K. Bold the wrong answers or let me know which ones I should double check and fix. Thanks for your help and I really appreciate it because there are no answers to these questions in the back of the book, so I need to know if they are correct. Thank you once again!

2. Originally Posted by skeske1234
Can someone please check my answers below for accurateness? The instructions are: Differentiate and simplify.

1) y=(2x^2+3x-1)(3x^2-5x-3)
y'=(4x+3)(3x^2-5x-3)+(2x^2+3x-1)(6x-5)
Differentiation was ok - but you should now simplify.

2) y=(5x^2+3x-1)(3x^2-5x-3)
y'=(10x+3)(4x^2-3)+(5x^2+3x-1)(8x)
Differentiation is not ok. Where on earth did you get that factor $4x^2-3$? The second factor was $(3x^2-5x-3)$, no?
And, again, you need to simplify.

3)y=6x^3-7x^2+5x-7+{\color{red}x^(5/3)}-7/(x^3)
y'=18x^2-14x+5+5x^(2/3)+21/(x^4)
Almost, but not quite: everything seems ok except the term $5x^{5/3}$. Think about it. Did you apply the power rule correctly? I don't think so.

4) y=[5x^4-3x^3+6x^2-5x+7-x^(3/2)]/x^2
y'=10x-3+5/(x^2)-14/(x^3)+1/(2((sqrt)x)^3)
Looks ok to me, but maybe one would want to ask whether some simplification is possible. Well, maybe - or maybe not.

5) y=(5x^2-3x+7)(3x^2+7x-2)(6x^2+4x-5)
y'=(10x-3)(3x^2+7x-2)(6x^2+4x-5)+(5x^2-3x+7)(6x+7)(6x^2+4x-5)+(5x^2-3x+7)(3x^2+7x-2)(12x+4)
Differentiation seems ok, but what about simplifying the whole mess? After all one might be able to collect same powers of x. $y$ is a polynomial of degree 6, therefore $y'$ must be a polynomial of degree $6-1=5$. I think it should be possible to make a polynomial of degree 5 look a little tidier on the page than this...

6) y=(7x^3-5x^2+6x-3)^12
y'=12(21x^2-10x+6)(7x^3-5x^2+6x-3)^11
Differentiation seems ok to me. (I'm a little surprised to see you put the "inner derivative" $21x^2-10x+6$ as the second factor here.) I don't think one would want to try to "simplify" here by multiplying out

7) y=(4x^2+3)^5(2x^2-1)^4
y'=[8x(4x^2+3)^4(2x^2-1)^3][5(2x^2-1)+2(4x^2+3)]
No, for some reason you have botched this one up completely. What about
$y'=5(4x^2+3)^4\cdot 8x\cdot (2x^2-1)^4+(4x^2+3)^5\cdot 4(2x^2-1)^3\cdot 4x$
Now here, you would simplify by factoring out $(4x^2+3)^4\cdot (2x^2-1)^3$

8) y=(4x^2+3x-5)^(4/5)
y'=
Judging from the above, you should be able to differentiate this one as well.

3. Originally Posted by Failure
Differentiation was ok - but you should now simplify.

Differentiation is not ok. Where on earth did you get that factor $4x^2-3$? The second factor was $(3x^2-5x-3)$, no?
And, again, you need to simplify.

Almost, but not quite: everything seems ok except the term $5x^{5/3}$. Think about it. Did you apply the power rule correctly? I don't think so.

Looks ok to me, but maybe one would want to ask whether some simplification is possible. Well, maybe - or maybe not.

Differentiation seems ok, but what about simplifying the whole mess? After all one might be able to collect same powers of x. $y$ is a polynomial of degree 6, therefore $y'$ must be a polynomial of degree $6-1=5$. I think it should be possible to make a polynomial of degree 5 look a little tidier on the page than this...

Differentiation seems ok to me. (I'm a little surprised to see you put the "inner derivative" $21x^2-10x+6$ as the second factor here.) I don't think one would want to try to "simplify" here by multiplying out

No, for some reason you have botched this one up completely. What about
$y'=5(4x^2+3)^4\cdot 8x\cdot (2x^2-1)^4+(4x^2+3)^5\cdot 4(2x^2-1)^3\cdot 4x$
Now here, you would simplify by factoring out $(4x^2+3)^4\cdot (2x^2-1)^3$

Judging from the above, you should be able to differentiate this one as well.
#1.. how do I simplify this? isn't it already in lowest terms
#2.. I used the the product rule to get that answer
3.. sorry in red supposed to be 5/3 x^(2/3) now correct?
8.. my answer is y'=[4(8x+3)]/[5(4x^2+3x-5)^1/5)] is this correct?

4. Originally Posted by skeske1234
#1.. how do I simplify this? isn't it already in lowest terms
Well, maybe your teacher has a different idea of what "simplifying" means. But if you multiply $y'$ out and collect same powers of $x$ you get $y'=24x^3 - 3x^2 - 48x - 4$. Looks simpler to me...

#2.. I used the the product rule to get that answer
No, you didn't. Because if you did, the second factor of the first term would look differently: as I wrote.

3.. sorry in red supposed to be 5/3 x^(2/3) now correct?
Yes.

8.. my answer is y'=[4(8x+3)]/[5(4x^2+3x-5)^1/5)] is this correct?
Yes.