# How to find derivative of $[1-F(v)]^{n}$ and $1-[1-F(v)]^{n}$?

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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Have you studied the chain rule? – David Mitra Feb 16 '12 at 22:26
Well, you have to show that by induction. – checkmath Feb 16 '12 at 22:41
Note: An "equation" must have an "equal" sign in it (hence the name). What you give are not "equations", they are expressions. – Arturo Magidin Feb 16 '12 at 22:43

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: $$\Big(1-(1-F(v))^n\Big)'=0-(-f(v)n(1-F(v))^{n-1})=f(v)n(1-F(v))^{n-1}$$