Chain Rule vs Product Rule

duki

I have a question more than a problem to answer.
I'm having a difficult time recognizing when to use the product rule and when to use the chain rule.

How do you recognize when to use each, especially when you have to use both in the same problem. Problems like [tex]y+x^4y^3-5x^6+3y^8-42=0[/tex] tend to mix me up.

rocomath

Product rule: x times y [tex]\frac{d}{dx}(xy)=xy'+y[/tex]

Chain rule: 2x+2 raised to the power of 2 [tex]\frac{d}{dx}(2x+2)^2=2(2x+2)\cdot2[/tex]

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duki	Chain Rule vs Product Rule I have a question more than a problem to answer. I'm having a difficult time recognizing when to use the product rule and when to use the chain rule. How do you recognize when to use each, especially when you have to use both in the same problem. Problems like [tex]y+x^4y^3-5x^6+3y^8-42=0[/tex] tend to mix me up.

rocomath	Product rule: x times y [tex]\frac{d}{dx}(xy)=xy'+y[/tex] Chain rule: 2x+2 raised to the power of 2 [tex]\frac{d}{dx}(2x+2)^2=2(2x+2)\cdot2[/tex]