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Find the derivatives of the given functions.$$y=\ln \left(x-x^{2}\right)^{3}$$

$\frac{d y}{d x}=\frac{3(1-2 x)}{x-x^{2}}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 5

Derivative of the Logarithmic Function

Derivatives

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University of Michigan - Ann Arbor

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we want to find dy dx for the function. Why is equal to the natural algorithm of x minus x squared cute. This question is since their knowledge of differentiation shortcuts related transcendental functions in particular those were logarithmic functions. So we have to note relevant rules to proceed on the left. I have the rules protecting DDX of log B of U n L. Interview on the right rules 123 are respectively the power rule. Product rule in changeable for this function Y equals x minus x, cuba square or rather cute. We already have it in its most easily defensible forum and we see that we're going to have to use rule zero G. D. Exelon you to solve for you is x minus X squared cute. Thus will have to also invoke the chain rule. So do I. D. S is one over you? One by one over X minus X squared cute times the U D X. Which is by the channel three times x minus x squared square terms one minus two X. Thus we have solution. Dy dx is equal to three minus six X divided by x minus x squared

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