# How do you find #dy/dx# by implicit differentiation of #x^2+y^2=36#?

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To find ( \frac{dy}{dx} ) by implicit differentiation of ( x^2 + y^2 = 36 ), follow these steps:

- Differentiate both sides of the equation with respect to ( x ).
- Use the chain rule for differentiating terms involving ( y ).
- Solve for ( \frac{dy}{dx} ) in terms of ( x ) and ( y ).

Starting with the given equation:

[ x^2 + y^2 = 36 ]

Differentiate both sides with respect to ( x ):

[ \frac{d}{dx}(x^2) + \frac{d}{dx}(y^2) = \frac{d}{dx}(36) ]

[ 2x + 2y \frac{dy}{dx} = 0 ]

Isolate ( \frac{dy}{dx} ) to solve for it:

[ 2y \frac{dy}{dx} = -2x ]

[ \frac{dy}{dx} = \frac{-2x}{2y} ]

[ \frac{dy}{dx} = \frac{-x}{y} ]

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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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