Implicit Differentiation Problem

• Feb 1st 2008, 09:30 AM
wannberocketscientist
Implicit Differentiation Problem
Hi,

This is the last one before everyone here thinks Im taking liberities!

Got this expression

cos y - x^2y^3 + 2y = pi

and have to put it in the form of f(x,y)

My understanding is that pi would disappear with it being a constant but I feel this is not right?

can the middle variables of x and y be sorted by using the product rule?

Sorry to put loads of posts up at once but Im playing catch up as being a fire fighter is not the best profession to have whilst learning calculus at home!

Cheers again
• Feb 1st 2008, 09:37 AM
galactus
You want to differentiate implicitly?. Yes, you can use the product rule on the middle term.

You get:

$\displaystyle -sin(y)\frac{dy}{dx}-3x^{2}y^{2}\frac{dy}{dx}-2xy^{3}+2\frac{dy}{dx}=0$

Now, solve for dy/dx.
• Feb 1st 2008, 09:38 AM
wannberocketscientist
nice one cheers
• Feb 1st 2008, 09:45 AM
wannberocketscientist
does :

3x^2/cos(y)(2y^2) look right or is that an utter cock up?
• Feb 1st 2008, 10:02 AM
colby2152
Quote:

Originally Posted by wannberocketscientist
does :

3x^2/cos(y)(2y^2) look right or is that an utter cock up?

Not sure what you did, but going from Galactus' work:

$\displaystyle -sin(y)\frac{dy}{dx}-3x^{2}y^{2}\frac{dy}{dx}-2xy^{3}+2\frac{dy}{dx}=0$

$\displaystyle (-sin(y)-3x^{2}y^{2}+2)\frac{dy}{dx}=2xy^{3}$

$\displaystyle \frac{dy}{dx}=\frac{2xy^{3}}{-sin(y)-3x^{2}y^{2}+2}$