How do I find the derivative of
y = ln(x) - 1
ln^2(x)
?? i tried so many ways... it never turns out right. according to the calculator anyway.
thanks in advance!
$\displaystyle y = (\ln(x) - 1) \cdot \frac{1}{(\ln(x))^2}$
$\displaystyle \frac{dy}{dx} = \frac{1}{x} \cdot (ln(x))^{-2} + \frac{-2(ln(x))^{-3}}{x} \cdot (ln(x)-1)$
Using the product rule.
Then Simplify to:
$\displaystyle \frac{dy}{dx} = \frac{1}{x(ln(x))^2}\{\frac{2}{ln(x)} - 1 \}$
Understand?