# Induction proof of nth derivative

1. Sep 22, 2008

### Bob Ho

Show by induction that the nth derivative f(n)(x) of;

f(x)=sqrt(1-x)

is

f(n)(x)= -$$\frac{(2n)!}{4^{n}n!(2n-1)}$$*(1-x)(1/2)-n

for n $$\geq$$ 1.

2. Sep 22, 2008

### uocan

For n=1 it works.

For n=k-1 assume that it works. Write n=kth derivative as the derivative of the expression for k-1, i.e d(f(k-1)(x))/(dx). Taking the derivative the result follows.

3. Sep 22, 2008

### Redbelly98

Staff Emeritus
Homework questions should be posted in the homework section of this forum.

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