How do you find the derivative of #y^2=1+x^2#?
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To find the derivative of ( y^2 = 1 + x^2 ), you can implicitly differentiate both sides of the equation with respect to ( x ). This yields:
[ \frac{d}{dx}(y^2) = \frac{d}{dx}(1 + x^2) ]
Using the chain rule on the left side, and differentiating the right side:
[ 2y \frac{dy}{dx} = 0 + 2x ]
Solving for ( \frac{dy}{dx} ), we get:
[ \frac{dy}{dx} = \frac{x}{y} ]
Therefore, the derivative of ( y^2 = 1 + x^2 ) with respect to ( x ) is ( \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.
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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