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How can I find the derivative with respect to $v$ for the following two equations: $[1-F(v)]^{n} \tag{1}$ and $1-[1-F(v)]^{n} \tag{2}$ where F'(v)=f(v)

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    Well, you have to show that by induction.2012-02-16

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By using the chain rule: \Big((1-F(v))^n\Big)'=(1-F(v))'n(1-F(v))^{n-1}=-f(v)n(1-F(v))^{n-1} Similarly: \Big(1-(1-F(v))^n\Big)'=0-(-f(v)n(1-F(v))^{n-1})=f(v)n(1-F(v))^{n-1}

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    got it, thank you so much!2012-02-16