# Implicit diff first or inverse trig first?

• Jan 28th 2007, 02:16 PM
ryanfoster
Implicit diff first or inverse trig first?
I am trying to diff wrt the following

A*arcsin(tan(3xy)+2)

where A is a contstant.

Can anybody help?
• Jan 28th 2007, 10:47 PM
CaptainBlack
Quote:

Originally Posted by ryanfoster
I am trying to diff wrt the following

A*arcsin(tan(3xy)+2)

where A is a contstant.

Can anybody help?

You are leaving us with a bit more guess work to do than I like.

What do you want to differentiate, and with respect to what?

RonL
• Jan 29th 2007, 03:18 PM
ryanfoster
Quote:

Originally Posted by CaptainBlack
You are leaving us with a bit more guess work to do than I like.

What do you want to differentiate, and with respect to what?

RonL

I would like to differentiate implicitly wrt to x :

y=arcsin(tan(3xy)+2)

Sorry about the lack of info - just getting back into mathematics after a 10 year gap
• Jan 29th 2007, 04:09 PM
topsquark
Quote:

Originally Posted by ryanfoster
I would like to differentiate implicitly wrt to x :

y=arcsin(tan(3xy)+2)

Sorry about the lack of info - just getting back into mathematics after a 10 year gap

Chain rule:
$\displaystyle y=asn(tan(3xy)+2)$

$\displaystyle \frac{dy}{dx} = \frac{1}{\sqrt{1 - (tan(3xy) + 2)^2}} \cdot (tan^2(3xy) + 1) \cdot \left (3y + 3x \frac{dy}{dx} \right )$

Now solve for $\displaystyle \frac{dy}{dx}$

-Dan