Calculus
posted by Anonymous .
1.) Find the derivative of tan (sec x).
2.) Find the derivative if 1/x in four ways, using the limit process, power rule, quotient rule and implicit differentiation.
3.) Show that the derivative of sec^1 x is 1/(x*sqrt(x^2 1)).
4. Find the derivative of 2^(e^(sin x)).
Thank you in advance.

d/du(tan u) = sec^2 u
so, use that and apply the chain rule:
sec^2(sec x) * secx tanx
I'm sure you can do #2
y = sec^1 x
sec y = x
secy tany y' = 1
y' = 1/(secy tany)
y' = 1/(x √(x^21))
y = 2^(e^(sinx))
y' = ln2 2^(e^(sinx)) * e^(sinx) * cosx
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