Question

I know that I have to apply the product or quotient rules for these problems but I'm not sure why I'm getting them wrong.
Please help me!
Find the derivative:
1) f(x) = x^6/108 times (6 ln(x) − 1)
I got: 6x^5 times 6 ln(x)-1 + x^6/108 times 6/x

2) f(x) = (ax + b)/(cx + k)
I got: x(cx+k) - (ax+b)x all over (cx+k) squared

3) y = 3x(ln x + ln 3) − 10x + e
I got: 3lnx + 3x/x - 10

Answer 1

1. f(x) = ((1/108)x^6)(6lnx - 1)

product rule:
f ' (x) = (1/108)x^6 (6/x) + (1/18)x^5 (6lnx - 1)
= (1/18)x^5 + (1/18)x^5)(6lnx - 1)
common factor of (1/18)x^5
= (1/18)x^5 (1 + 6lnx - 1)
= (1/3) x^5 lnx

check:
http://www.wolframalpha.com/input/?i=derivative+%28%281%2F108%29x%5E6%29%286lnx+-+1%29

2. y = (ax+b)/(cx+k) , where a, b,c, and k are constants
y' = ( a(cx+k) - c(ax+b) )/(cx+k)^2
= (acx + ak - acx - bc)/(cx+k)^2
= (ak - bc)/(cx+k)^2

3.
y = 3xlnx + 3ln3 x - 10x + e
y' = 3x(1/x) + 3lnx + 3ln3 - 10
= 3 + 3lnx + 3ln3 - 10
= 3lnx + 3ln3 - 7
= 3(lnx + ln3) - 7
= 3ln(3x) - 7

looks like you have some major studying ahead of you

Answer 2

Oh wow, I was really off. Thank you so much for explaining it to me!