# How do you implicitly differentiate # x^2+x/y-xy^2+x=3y #?

But from Eqn(1)

The differentiated equation is:

Collecting like terms

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To implicitly differentiate the given equation ( x^2 + \frac{x}{y} - xy^2 + x = 3y ), follow these steps:

- Differentiate each term of the equation with respect to ( x ).
- Apply the product rule and chain rule where necessary.
- Solve for the derivative.

The implicit differentiation of the given equation yields:

[ 2x + \left( \frac{1}{y} - y^2 \right) - y^2 - x + 1 = 3 \frac{dy}{dx} ]

Simplify the equation to isolate ( \frac{dy}{dx} ):

[ \frac{dy}{dx} = \frac{2x + \frac{1}{y} - 2y^2 - x + 1}{3} ]

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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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- How do you implicitly differentiate #-1=y^2-(x-e^y)/(y)#?
- How do you differentiate #f(x) = (2x+1)(4-x^2)(1+x^2) #?

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