# How would you derive this??

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• Sep 8th 2007, 08:55 PM
runner07
How would you derive this??
ok so here is the function (we're working with hyperbolic trig)....

y= arctan(sinhx)

so i'm thinking we do product rule here? but then, what's the derivative of arctan? is there one?
• Sep 8th 2007, 08:58 PM
Jhevon
Quote:

Originally Posted by runner07
ok so here is the function (we're working with hyperbolic trig)....

y= arctan(sinhx)

so i'm thinking we do product rule here? but then, what's the derivative of arctan? is there one?

the derivative of arctan(x) is something you can find in your text.

$\displaystyle \frac {d}{dx} \arctan u = \frac {u'}{1 + u^2}$
• Sep 8th 2007, 09:00 PM
runner07
oh wow that completely slipped my mind. thanks!
• Sep 8th 2007, 09:03 PM
Krizalid
Quote:

Originally Posted by runner07
y= arctan(sinhx)

Or you can take $\displaystyle \tan y=\sinh x$, that also makes sense.
• Sep 8th 2007, 09:13 PM
Jhevon
Quote:

Originally Posted by Krizalid
Or you can take $\displaystyle \tan y=\sinh x$, that also makes sense.

yes. and, of course, you would have to do implicit differentiation here