How Do You Differentiate x^2y and xy^2?

[afcwestwarrior]

x^2y

the y is biglike the x its not small

and how do you differentiate this
xy^2

for the first one i used the product rule and thesecond one and i get a different answer then what i was suppost to get

 

[afcwestwarrior]

for the first one i didthis

x^2 d/dx y dy/dx + y d/dx x^2

x^2 y' + y+ 2x

so how come I am not getting 2x 2y

 

[Werg22]

You need an equation, not an expression, i.e. $$x^{2}y = ?$$. Also, are you familiar with implicit differentiation?

 

[afcwestwarrior]

ill give u the equation x^3+x^2y+4y^2=6

 

[afcwestwarrior]

i understand it now, the answer of this was factored out or cleaned up a bit, so i didn't notice there was an x outside of the paranthesis of 2y

 

[Werg22]

$$x^3 + x^2y + 4y^2 = 6$$

Okay, but do you know what implicit differentiation is? For example,

[tex]x + y = 1 [/itex]

$$\frac{dx}{dx} + \frac{dy}{dx} = \frac{d1}{dx}$$

$$1 + \frac{dy}{dx} = 0$$

Also for a product, the product rule applies, e.g.

$$xy = 1$$

$$x*\frac{dy}{dx} + \frac{dx}{dx}*y = 0$$