Implicit Differentiation Problem

**wannberocketscientist** · February 1st 2008, 09:30 AM

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

**galactus** · February 1st 2008, 09:37 AM

You want to differentiate implicitly?. Yes, you can use the product rule on the middle term.

You get:

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

Now, solve for dy/dx.

**wannberocketscientist** · February 1st 2008, 09:38 AM

nice one cheers

**wannberocketscientist** · February 1st 2008, 09:45 AM

does :

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

**colby2152** · February 1st 2008, 10:02 AM

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:

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

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

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

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