Please help answer this question:
"Obtain a formula for the nth derivative of the product of two functions, and prove the formula by induction on n."
Any educated tries are appreciated.
If you take two functions, f and g, and find the first, second and third
derivative of fg you should see the binomial coeficients and come up with a
Here designates the jth derivative of f and .
It is clear that this is valid if n=1 and hence for the induction step calculate
But so we get
Since we can write this
which is the hypothezised expression for the (n+1)st derivative of fg. Thus
for all positive integers n.
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