How do you differentiate #y=x^2yy^2x#?
I found:
In your case we get:
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To differentiate the given expression, ( y = x^2y  y^2x ), with respect to ( x ), you can use the product rule and the chain rule:

Apply the product rule to ( x^2y ) and ( y^2x ). [ \frac{d}{dx}(x^2y) = 2xy + x^2\frac{dy}{dx} ] [ \frac{d}{dx}(y^2x) = y^2  2xy\frac{dy}{dx} ]

Combine the results. [ \frac{d}{dx}(y) = 2xy + x^2\frac{dy}{dx}  y^2  2xy\frac{dy}{dx} ]

Simplify the expression. [ \frac{d}{dx}(y) = (2xy  2xy)\frac{dy}{dx} + (x^2  y^2) ]

Further simplify to get the final answer. [ \frac{d}{dx}(y) = (x^2  y^2) ]
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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