# How do you differentiate #x^4+4x^3y+y^4=1#?

You must remember that when deriving

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To differentiate the equation ( x^4 + 4x^3y + y^4 = 1 ) with respect to ( x ), use implicit differentiation. The derivative of each term with respect to ( x ) is:

[ 4x^3 + 12x^2 \frac{dy}{dx} + 4y \frac{dy}{dx} = 0 ]

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

[ 12x^2 \frac{dy}{dx} + 4y \frac{dy}{dx} = -4x^3 ]

[ \frac{dy}{dx}(12x^2 + 4y) = -4x^3 ]

[ \frac{dy}{dx} = \frac{-4x^3}{12x^2 + 4y} ]

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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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