1. ## 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

2. 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.

3. nice one cheers

4. does :

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

5. 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:

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

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

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