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The n-th derivative of the product of two functions example

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A formula is derived for the n-th derivative of a function that is a product of two other functions, f(x)=u(x).v(x)

This formula is used to write down the n-th derivative of f(x) = e^x/(1 − x).

The proof of the result used is by mathematical induction on 'n'.

The solution is typed neatly and comes as a pdf file.

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Solution Summary

The problem is solved in two stages. First a general result is proved, that of the n-th derivative of a function f(x)=u(x)v(x).

Then this formula is applied to the specific example in the question.

The result is used to write down the three first derivatives as requested in the question.

Solution Preview

Note: the attachment has a typed pretty version of the solution.

A formula for the $n$-th derivative of the function f(x)=u(x)v(x) is derived in the appendix.

Let v=e^x and ...

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