Question

find the slope of the of the curve.
y = 1 / (x-1) at x = 2

Answer 1

Slope of a function is it's first derivative. So:
m=dy/dx=d(x-1)^-1 /dx=-1(x-1)^-2
m=-1/(x-1)^2
Plug 2 into this eq to find m at x=2

Answer 2

ok i need help finding the derivative

Answer 3

i use the \[\lim_{h \rightarrow 0} \frac{ f(x+h) - f(x)}{ h} \] right?

Answer 4

Correct, taht's the definition of derivative. Or simply:
\[\frac{du^n}{dx}=n u^{n-1}*\frac{du}{dx}\]

Answer 5

In this case, you have to use something called the quotient rule:\[\frac d{dx}\left[\frac{g(x)}{h(x)}\right]=\frac{g'(x)h(x)-g(x)h'(x)}{h^2(x)}.\]