Posted by lala on Tuesday, April 13, 2010 at 4:01pm.
How do i find the second derivative of f(x)= tan(1x)^1/2

Calculus  Reiny, Tuesday, April 13, 2010 at 5:32pm
f'(x) = (1/2)(tan(1x))^(1/2)*sec^2 (1x)(1)
= (1/2) [tan(1x)]^(1/2) [sec(1x)]^2
now we need the product rule, what a mess ...
f''(x) = (1/2) [tan(1x)]^(1/2) (2)(sec(1x)) (sec(1x))(tan(1x))(1) + (1/2)[sec(1x)]^2 (1/2)tan(1x))^(3/2)(sec^2(1x))(1)
check this carefully and see if you simplify by factoring. I can see all kinds of common factors, but find it hard to read my own typing, lol
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