# How do you implicitly differentiate # sqrt(3x+3y) + sqrt(3xy) = 17.5#?

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To implicitly differentiate the equation sqrt(3x+3y) + sqrt(3xy) = 17.5, follow these steps:

- Differentiate each term of the equation with respect to both x and y.
- Use the chain rule for differentiating the square root terms.
- Solve for the derivatives.

The result of implicit differentiation for this equation with respect to x and y respectively is:

For ( \frac{dx}{dy} ): [ \frac{dx}{dy} = -\frac{3x + 3y}{3x + 6y + 3\sqrt{3x + 3y}} - \frac{3y}{3x + 6y + 3\sqrt{3xy}} ]

For ( \frac{dy}{dx} ): [ \frac{dy}{dx} = -\frac{3x}{3x + 6y + 3\sqrt{3x + 3y}} - \frac{3x + 3y}{3x + 6y + 3\sqrt{3xy}} ]

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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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