How do you differentiate #(y1)^2+x=0#?
dy/dx=1/(2(y1)#
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To differentiate ( (y  1)^2 + x = 0 ) implicitly with respect to ( x ), follow these steps:

Differentiate each term of the equation with respect to ( x ).

For the term ( (y  1)^2 ), you need to use the chain rule. The derivative of ( (y  1)^2 ) with respect to ( x ) is ( 2(y  1) \frac{dy}{dx} ).

For the term ( x ), the derivative is ( 1 ).

Set up the equation with the derivatives and solve for ( \frac{dy}{dx} ).
[ 2(y  1) \frac{dy}{dx} + 1 = 0 ]
[ 2(y  1) \frac{dy}{dx} = 1 ]
[ \frac{dy}{dx} = \frac{1}{2(y  1)} ]
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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