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Let's find the derivative of F of Z equals e
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to the T oversee minus one. And in general
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, the derivative of E to a function is each
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of that function times the derivative of that function.
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So the derivative here should be e to the Z
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over Z minus one times the derivative of the over
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Z minus one. So to find the derivative of
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the over Z minus one, we can use the
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quotient rule. So we have the bottom Z minus
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one times the derivative of the top one, minus
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the top Z times. The derivative of the bottom
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, the derivative of Z minus one would be one
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over the bottom squared so over Z minus one squared
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. Now we can simplify that. So simplifying the
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numerator Z minus one minus Z would just be negative
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one so altogether than are derivative is negative one times
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e to the C over Z minus one over C
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minus one quantity squared