Purchase Solution

# Real Analysis: Differential Equations (Leibnitz Formula)

Not what you're looking for?

Let I be an open interval and n be a natural number. Suppose that both f:I->R and g:I->R have n derivatives. Prove that fg:I->R has n derivatives, and we have the following formula called Leibnitz's formula:

(fg)^n(x) = the sum as k=0,1,2,...n of(n choose k)f^k(x)g^(n-k)(x) for all x in I.

Write the formula out explicitly for n=2 and n=3.

##### Solution Summary

Leibnitz's formula is used to prove a relationship between derivatives of two functions. The solution is detailed and well presented.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Probability Quiz

Some questions on probability