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Use logarithmic differentiation to find dy/dx. y = (x + 1)(x - 10)/(x - 1)(x + 10) x > 10 dx/dy =

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Final answer:

To find dy/dx using logarithmic differentiation, take the natural logarithm of both sides of the equation and apply logarithmic properties. Then, differentiate both sides using the chain rule.

Step-by-step explanation:

To find dy/dx using logarithmic differentiation, we first take the natural logarithm of both sides of the equation y = (x + 1)(x - 10)/(x - 1)(x + 10):

ln(y) = ln((x + 1)(x - 10)/(x - 1)(x + 10))

Next, we use logarithmic properties to simplify the expression:

ln(y) = ln(x + 1) + ln(x - 10) - ln(x - 1) - ln(x + 10)

To differentiate both sides with respect to x, we use the chain rule:

(1/y) * (dy/dx) = (1/(x + 1)) + (1/(x - 10)) - (1/(x - 1)) - (1/(x + 10))

Multiplying both sides by y gives us:

dy/dx = y * [(1/(x + 1)) + (1/(x - 10)) - (1/(x - 1)) - (1/(x + 10))]

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