1. ## quick differentiation :)

hey guys, quick question, how do you use the product rule to differentiate something with more than 2 terms... for example:

3x^2y^3

I think I'm finally gettin the hang of this stuff guys thanks for all the help

2. Originally Posted by shepherdm1270
hey guys, quick question, how do you use the product rule to differentiate something with more than 2 terms... for example:

3x^2y^3

I think I'm finally gettin the hang of this stuff guys thanks for all the help
That is two terms, but say you have the following...

$\displaystyle \sin(x)e^x x^2$

This is a product of three terms. You always split products into two terms like so:

$\displaystyle \sin(x) * e^x x^2$

The derivative follows the product rule TWICE over...

$\displaystyle \cos(x) e^x x^2 + (e^x x^2)' \sin(x)$

$\displaystyle \cos(x) e^x x^2 + \sin(x)(e^x x^2 + 2x e^x)$

3. hmmm... ok so using implicit differentiation for this problem i got this so far:

x^4 + 3 x^2 y^3 - y^2 = 5

d/dx ( x^4 + 3 x^2 y^3 - y^2) = d/dx (5)

4x^3 + (this is where I get messed up)

is it (3x^2)(3y^2 dy/dx) + (y^3)(6x)???