# How do you use implicit differentiation to find #(dy)/(dx)# given #1=3x+2x^2y^2#?

So:

Differentiating gives:

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To find (\frac{{dy}}{{dx}}) using implicit differentiation for the equation (1 = 3x + 2x^2y^2), follow these steps:

- Differentiate both sides of the equation with respect to (x).
- Apply the chain rule where necessary.
- Solve the resulting equation for (\frac{{dy}}{{dx}}).

The derivative of the equation (1 = 3x + 2x^2y^2) with respect to (x) yields:

[0 = 3 + 4xy^2\frac{{dy}}{{dx}}]

Solve for (\frac{{dy}}{{dx}}):

[\frac{{dy}}{{dx}} = -\frac{3}{{4xy^2}}]

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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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