How do you differentiate this

In summary, the conversation is discussing the differentiation of x^2y and xy^2, using the product rule and implicit differentiation. The correct answer for x^2y was achieved after factoring out an x from the equation. The concept of implicit differentiation was also briefly mentioned.
  • #1
afcwestwarrior
457
0
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
 
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  • #2
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
 
  • #3
:confused: You need an equation, not an expression, i.e. [tex]x^{2}y = ?[/tex]. Also, are you familiar with implicit differentiation?
 
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  • #4
ill give u the equation x^3+x^2y+4y^2=6
 
  • #5
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
 
  • #6
[tex]x^3 + x^2y + 4y^2 = 6[/tex]

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

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

[tex]\frac{dx}{dx} + \frac{dy}{dx} = \frac{d1}{dx} [/tex]

[tex]1 + \frac{dy}{dx} = 0 [/tex]

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

[tex]xy = 1[/tex]

[tex]x*\frac{dy}{dx} + \frac{dx}{dx}*y = 0 [/tex]
 
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