# easy differentiation?

• Jun 1st 2009, 04:11 AM
djmccabie
easy differentiation?
ok i Just came out of an exam an wondering if I differentiated part of a question right.

I know

$tan(x)$ differentiates to $sec^2x$

but would $tan(2x)$ differentiate to $2sec^22x$ or $2sec^24x$?
• Jun 1st 2009, 04:12 AM
Moo
Hello,
Quote:

Originally Posted by djmccabie
ok i Just came out of an exam an wondering if I differentiated part of a question right.

I know

$tan(x)$ differentiates to $sec^2x$

but would $tan(2x)$ differentiate to $2sec^22x$ or $2sec^24x$?

To $2\sec^2(2x)$

Use the chain rule : $[u(v(x))]'=v'(x)u'(v(x))$

Here, $v(x)=2x$ and u=tan
• Jun 1st 2009, 05:22 AM
Showcase_22
$\frac{d}{dx} \tan 2x= 2\sec^2 2x$