# How do you find the derivative of #5=3e^(xy)+x^2y+xy^2#?

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To find the derivative of the equation (5 = 3e^{xy} + x^2y + xy^2), you would use implicit differentiation. Taking the derivative of both sides of the equation with respect to (x), you would differentiate each term individually, treating (y) as a function of (x) and applying the chain rule where necessary. The result will be the derivative of (y) with respect to (x), which represents the slope of the tangent line to the curve at any point.

The derivative of (3e^{xy}) with respect to (x) using the chain rule is (3ye^{xy}). The derivative of (x^2y) with respect to (x) is (2xy + x^2\frac{dy}{dx}) by the product rule. The derivative of (xy^2) with respect to (x) is (y^2 + 2xy\frac{dy}{dx}) by the product rule.

Now, you can rearrange the equation and solve for (\frac{dy}{dx}), the 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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