How do you differentiate #x^(2/3)+y^(2/3)=4#?
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To differentiate the equation (x^{2/3} + y^{2/3} = 4) implicitly with respect to (x), you would follow these steps:
 Differentiate each term of the equation with respect to (x).
 Use the chain rule for differentiating terms involving (y) with respect to (x).
 Solve for (\frac{{dy}}{{dx}}) to find the derivative.
Starting with the given equation (x^{2/3} + y^{2/3} = 4), the steps are as follows:

Differentiate each term: [ \frac{{d}}{{dx}}(x^{2/3}) + \frac{{d}}{{dx}}(y^{2/3}) = \frac{{d}}{{dx}}(4) ]

Apply the chain rule for terms involving (y): [ \frac{{2}}{{3}}x^{1/3}\frac{{dx}}{{dx}} + \frac{{2}}{{3}}y^{1/3}\frac{{dy}}{{dx}} = 0 ]

Solve for (\frac{{dy}}{{dx}}): [ \frac{{dy}}{{dx}} = \frac{{x^{1/3}}}{{y^{1/3}}}]
This is the derivative of (y) with respect to (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.
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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