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How do you differentiate #x^2 + 9y^2 = 1#?

Answer 1

Cameron Alexander

#dy/dx=-x/(9y)#

#x^2+9y^2=1#

By implicit differentiation #2x+9*2y*dy/dx =0#

#18y*dy/dx=-2x#

#dy/dx=-x/(9y)#

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Answer 2

Christopher Allers

To differentiate the equation (x^2 + 9y^2 = 1), you need to take the derivative of both sides of the equation with respect to the variable you're differentiating. Since there's only one variable, which is either (x) or (y), you can treat the other variable as a constant. Let's differentiate with respect to (x) for this equation:

[\frac{d}{dx}(x^2) + \frac{d}{dx}(9y^2) = \frac{d}{dx}(1)]

[2x + 9 \frac{dy}{dx}(2y) = 0]

[2x + 18y \frac{dy}{dx} = 0]

[2x = -18y \frac{dy}{dx}]

[\frac{dy}{dx} = \frac{-2x}{18y}]

[\frac{dy}{dx} = \frac{-x}{9y}]

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Answer from HIX Tutor

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.