If f(t)= √((t^2-1)/(t^2-1))
Find f '(t)
I have tried it several times using f(x+h)-f(x) / h, but I always get lost and don't know how to solve it.
Could someone help me?
Thank you
Why dont you just use the rules of differntiation?
I dont see why you would try to find the derivative of f using the limit definition of the derivative.
Two obvious approaches that stand out.
first you could use the chain rule followed by the quotient rule for differentiation.
or simplify
$\displaystyle f(t)=\sqrt {\frac{t^2-1}{t^2 + 1} } = \frac{\sqrt {t^2-1}} {\sqrt{t^2 + 1}}$
then use the quotient rule and chain rule.
I find after some quick and sloppy calculations (so forgive me if this is not completely accurate)
$\displaystyle f'(t) = \frac{2t}{(t^2 - 1)(t^2 + 1)^{3/2}}$