# How do you implicitly differentiate #x^4+2y^2=8 #?

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To implicitly differentiate the equation (x^4 + 2y^2 = 8):

- Differentiate each term of the equation with respect to (x).
- Treat (y) as a function of (x) and apply the chain rule whenever differentiating (y).

Differentiating (x^4) with respect to (x) yields (4x^3). Differentiating (2y^2) with respect to (x) yields (4y \frac{dy}{dx}) by the chain rule. The derivative of a constant (in this case, 8) is 0.

So, the implicit differentiation of (x^4 + 2y^2 = 8) is (4x^3 + 4y \frac{dy}{dx} = 0).

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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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