How do you implicitly differentiate #x+xy2x^3 = 2#?
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To implicitly differentiate (x + xy  2x^3 = 2), follow these steps:
 Differentiate each term with respect to (x).
 Apply the chain rule whenever differentiating terms involving (y).
 Collect terms involving (y') on one side of the equation.
 Solve for (y').
The steps are as follows:

Differentiate each term:
[ \frac{d}{dx}(x) + \frac{d}{dx}(xy)  \frac{d}{dx}(2x^3) = \frac{d}{dx}(2) ]
[ 1 + x \frac{dy}{dx} + y  6x^2 = 0 ]

Rearrange terms:
[ x \frac{dy}{dx} + y = 1 + 6x^2 ]

Solve for (y'):
[ \frac{dy}{dx} = \frac{1 + 6x^2  y}{x} ]
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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.
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