# How do you find #(dy)/(dx)# given #x^2y^3-3y=x^2#?

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To find (\frac{{dy}}{{dx}}), you first differentiate the given equation with respect to (x) implicitly. Then, you solve for (\frac{{dy}}{{dx}}).

Differentiating the given equation (x^2y^3 - 3y = x^2) with respect to (x) implicitly, you get:

[2xy^3 + 3x^2y^2\frac{{dy}}{{dx}} - 3\frac{{dy}}{{dx}} = 2x]

Now, solve for (\frac{{dy}}{{dx}}):

[3x^2y^2\frac{{dy}}{{dx}} - 3\frac{{dy}}{{dx}} = 2x - 2xy^3]

[ \frac{{dy}}{{dx}}(3x^2y^2 - 3) = 2x - 2xy^3]

[\frac{{dy}}{{dx}} = \frac{{2x - 2xy^3}}{{3x^2y^2 - 3}}]

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When evaluating a one-sided 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 one-sided 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 one-sided 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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