# How do you implicitly differentiate #7=3x-y+y^2x#?

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To implicitly differentiate (7 = 3x - y + y^2x), follow these steps:

- Differentiate each term of the equation with respect to (x).
- Apply the chain rule whenever differentiating terms involving (y).
- Collect terms involving (y') on one side and terms not involving (y') on the other side.
- Solve for (y') (the derivative of (y) with respect to (x)).

Differentiating each term with respect to (x):

(d/dx [7] = d/dx [3x] - d/dx [y] + d/dx [y^2x])

Simplify the derivatives:

(0 = 3 - \frac{dy}{dx} + y^2 + 2xy\frac{dy}{dx})

Rearrange the equation:

(\frac{dy}{dx} - 2xy\frac{dy}{dx} = 3 + y^2)

Factor out (\frac{dy}{dx}):

(\frac{dy}{dx} (1 - 2xy) = 3 + y^2)

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

(\frac{dy}{dx} = \frac{3 + y^2}{1 - 2xy})

This is the implicit derivative of (y) with respect to (x).

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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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