# How do you find #dy/dx# by implicit differentiation given #xy^3=y+x#?

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To find dy/dx by implicit differentiation for the equation xy^3 = y + x, differentiate both sides of the equation with respect to x. Then, solve for dy/dx.

Differentiating both sides with respect to x gives:

(1)(y^3) + (x)(3y^2(dy/dx)) = (dy/dx) + 1

Simplify and solve for dy/dx.

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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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