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!
Differentiation was ok - but you should now simplify.
Differentiation is not ok. Where on earth did you get that factor ? The second factor was , no?2) y=(5x^2+3x-1)(3x^2-5x-3)
y'=(10x+3)(4x^2-3)+(5x^2+3x-1)(8x)
And, again, you need to simplify.
Almost, but not quite: everything seems ok except the term . Think about it. Did you apply the power rule correctly? I don't think so.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)
Looks ok to me, but maybe one would want to ask whether some simplification is possible. Well, maybe - or maybe not.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)
Differentiation seems ok, but what about simplifying the whole mess? After all one might be able to collect same powers of x. is a polynomial of degree 6, therefore must be a polynomial of degree . I think it should be possible to make a polynomial of degree 5 look a little tidier on the page than this...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 to me. (I'm a little surprised to see you put the "inner derivative" as the second factor here.) I don't think one would want to try to "simplify" here by multiplying out6) y=(7x^3-5x^2+6x-3)^12
y'=12(21x^2-10x+6)(7x^3-5x^2+6x-3)^11
No, for some reason you have botched this one up completely. What about7) 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)]
Now here, you would simplify by factoring out
Judging from the above, you should be able to differentiate this one as well.8) y=(4x^2+3x-5)^(4/5)
y'=
Well, maybe your teacher has a different idea of what "simplifying" means. But if you multiply out and collect same powers of you get . Looks simpler to me...
No, you didn't. Because if you did, the second factor of the first term would look differently: as I wrote.#2.. I used the the product rule to get that answer
Yes.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?