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!
On number 2, I believe you copied the question incorrectly.
Many of the problems can be simplified by foiling and adding terms (#1, 2 for example)
#2 is completly wrong
#3 has the wrong coefficent for the x^(2/3) term
#7 looks suspicious
#7 is correctly differentiated and simplified
Let's go through each problem and check the answers:
1) y=(2x^2+3x-1)(3x^2-5x-3)
y'=(4x+3)(3x^2-5x-3)+(2x^2+3x-1)(6x-5)
This seems to be correct.
2) y=(5x^2+3x-1)(3x^2-5x-3)
y'=(10x+3)(4x^2-3)+(5x^2+3x-1)(8x)
This seems to be correct.
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)
This seems to be correct.
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)
There seems to be an error. The last term should be 1/(2(sqrt{x^3})), not 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)
This seems to be correct.
6) y=(7x^3-5x^2+6x-3)^12
y'=12(21x^2-10x+6)(7x^3-5x^2+6x-3)^11
This seems to be correct.
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)]
This seems to be correct.
8) y=(4x^2+3x-5)^(4/5)
y'=[4(8x+3)]/[5(4x^2+3x-5)^(1/5)]
This seems to be correct.
Overall, most of the answers seem to be correct. Only question 4 has a minor error, which is the last term in the derivative. Please double-check and fix it as 1/(2(sqrt{x^3})).