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i take it you guys haven't gone over chain rule and all that nice stuff. Once you stop using the limit formula to calculate derivatives, things become much easier.
remember some simple facts, and it'll help you a lot.
d/dx ( x^a) = a*x^(a-1)
d/dx [f(x)*g(x)] = [d/dx f(x) ]g(x) + f(x)[d/dx g(x)]
d/dx[f(x) + g(x)] = d/dx f(x) + d/dx g(x)
d/dx [f(g(x))] = f'(g(x)) * g'(x)
where f(x) and g(x) are functions of x and ' signifies a derivative.
now you can take any derivative of any combination of polynomial functions.
so,
y(x)=(x-1)/(x-2)
=(x-1)*(x-2)^(-1)
dy/dx=1*(x-2)^(-1) + (x-1)*(-1)(x-2)^(-2)*1
dy/dx @x=3 -> (3-2)^(-1)+(3-1)*(-1)(3-2)^(-2)
=1+(2)*(-1) = -1
__________________
And if you say to me tomorrow, oh what fun it all would be.
Then what's to stop us, pretty baby. But What Is And What Should Never Be.
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