How do you find the second derivative of #xy =32#?
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To find the second derivative of the equation xy = 32, first, differentiate the equation with respect to x using the product rule. Then, differentiate the resulting equation again with respect to x to find the second derivative.

Differentiate xy = 32 with respect to x: d(xy)/dx = d(32)/dx y + x(dy/dx) = 0

Solve for dy/dx: dy/dx = y/x

Differentiate dy/dx with respect to x: d(dy/dx)/dx = d(y/x)/dx d^2y/dx^2 = (1/x) * (dy/dx) + y/x^2

Substitute dy/dx from step 2 into the equation: d^2y/dx^2 = (1/x) * (y/x) + y/x^2 = (y/x^2) + y/x^2 = (2y/x^2)
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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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