#2) Use quotient rule
[tex]\frac{f'g - fg'}{g^2}[/tex]
Remember for solving log equations:
[tex]e^{ln x} = x[/tex]
#3) Derivative of tan = sec^2 = 1/cos^2
Domain of tan is [-pi/2, pi/2], only consider x values in that domain.
#4 Use Quotient rule
#9 Use double angle identity for tan
[tex]tan(2x) = \frac{2tan x}{1-tan^2 x} [/tex]
This way you can rewrite tan(pi/2) in terms of tan(pi/4).
Next use L'hopitals rule, which says the limit of indeterminate form(0/0) equals limit of quotient of derivatives of top/bottom of fraction.
Take derivative of both top part and bottom part separately, then reevaluate the limit.
