Second Derivitive Prob: find f" for f(x)=3ln[sec(x)+tan

[rofl]

f(x)=3ln[sec(x)+tan(x)]

f''(x)=?

 

[daon]

A TI-89 could do this for you. In fact if you knew the anti-derivative and derivative of sec(x) the answer is clear immediately.

 

[stapel]

f(x)=3ln[sec(x)+tan(x)]

f''(x)=?

What did you get for the first derivative?

Where are you stuck?

Please be specific. Thank you.

Eliz.

 

[imnerd]

is the answer 3 tan x sec x?

 

[stapel]

is the answer 3 tan x sec x?

Yes.

Eliz.

 

[soroban]

Re: Second Derivitive Prob: find f" for f(x)=3ln[sec(x)

Hello, rofl!

Simplify as you work . . .

\(\displaystyle f(x)\;=\;3\cdot\ln[\sec(x)\,+\,\tan(x)]\)
Find \(\displaystyle f''(x)\)

First derivative: \(\displaystyle \L\:f'(x)\:=\:3\,\cdot\,\frac{\sec(x)\tan(x)\,+\,\sec^2(x)}{\sec(x)\,+\,\tan(x)}\)

. . Factor and reduce: \(\displaystyle \L\:3\,\cdot\,\frac{\sec(x)\,\left[\sout{\tan(x)\,+\,\sec(x)}\right]}{\sout{\sec(x)\,+\,\tan(x)}} \;=\;3\cdot\sec(x)\;\) . . . see?


Second derivative: \(\displaystyle \L\:f''(x)\;=\;3\cdot\sec(x)\cdot\tan(x)\)