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y is composite of two functions " lnx" " and (1 - 2x)^3
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Let u(x)= lnx " and " v(x) = (1-2x)^3"
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Then, " y=u(v(x))"
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Differentiating this function is determined by applying chain rule.
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color(red)(y' = u'(v(x))xxu'(x))
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color(red)(u'(v(x)) = ?)
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u'(x) = 1/x
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u'(v(x))) = 1/(v(x))
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color(red)(u'(v(x)) = 1/(1-2x)^3)
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color(red)(v'(x) = ?)
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v'(x) = 3(1-2x)^2(1-2x)'
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v'(x) = 3(1-2x)^2(-2)
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color(red)(v'(x) = -6(1-2x)^2)
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color(red)(y' = u'(v(x))xxu'(x))
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y' = 1/(1-2x)^3 xx -6(1-2x)^2
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y' = (-6(1-2x)^2)/(1-2x)^3
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y' = -6/(1-2x)
