I am currently taking calc 2 because I am lazy and wanted to hold off taking calc 2 because calc one gave me some trouble. I am a mechanical engineering student and I need some help with this one problem. So far I got 18 out of the 19 questions correct, this one is just killing me and I think its just a silly mistake.

 

Thank you

Just apply the quotient rule:

 

[math]f(x) = \frac{g(x)}{h(x)} \Rightarrow f'(x) = \frac{h'(x)g(x) - g'(x)h(x)}{(h(x))^2}[/math]

 

So set [imath]g(x) = x[/imath], [imath]h(x) = 1 - \ln(x-1)[/imath], work out their derivatives and go from there.

Just apply the quotient rule:

 

[math]f(x) = \frac{g(x)}{h(x)} \Rightarrow f'(x) = \frac{h'(x)g(x) - g(x)h'(x)}{(h(x))^2}[/math]

 

So set [imath]g(x) = x[/imath], [imath]h(x) = 1 - \ln(x-1)[/imath], work out their derivatives and go from there.

 

Small, but significant typo there Dave. The second term in the numerator should be g'h not gh'

 

[math]f(x) = \frac{g(x)}{h(x)} \Rightarrow f'(x) = \frac{h'(x)g(x) - g'(x)h(x)}{(h(x))^2}[/math]

Quite right. Thanks for that.