Leibniz Definition and 63 Threads

[SOLVED] Leibniz' Integral rule Homework Statement Use the Leibniz' integral rule for differentiating under the integral sign to determine constants a and b such that the integral \int^{1}_{0}(ax+b-x^{2})^{2} dx is as small as possible. Homework Equations Leibniz' Interation was...

Question about the use of Leibniz notations … The following article states http://www.analyzemath.com/calculus/Differential_Equations/first_order.html u(x)*dy/dx=d(y*u)/dx So what i wonder is, how can you go from u(x)*dy/dx to d(y*u)/dx ... Kindly Pellefant ...

[SOLVED] a question on derivatives of leibniz find the 50th derivetive of the function f(x)=(x^2 * sin x) i don't know how this stuff work can you please show how to solve this question step by step

----EDIT------ In my original post I totally messed up my variables. Here I'll get straight to the point. I guess what I am really asking is how is \frac{dy/dx}{y-900} equal to \frac{d}{dx}ln|y-900| I know that the integral of \frac{1}{y-900} is ln|y-900| but I don't understand how the...

Homework Statement I found a purely epsilon-N proof of the Leibniz criterion for alternate series and it is quite inelegant compared to the classical proof so no wonder I never saw it in any textbook. But at the same time I must wonder if I made a mistake somewhere. The statement of the...

Leibniz notation is made of ratios of differential operators? right? what does this mean? What is a differential operator? Why can we take this ratio? In a u subsitution, why can we break apart du/dx? this doesn't make sense!

This question comes from how Leibniz chose his notation. How to prove that the limit when h goes to 0 of the expression: \frac{f(x + 2h) - f(x + h) - [f(x + h) - f(x)]}{h^{2}} is f''(x)? Step 1: We know that \frac{f(x + h) - f(x)}{h} = f'(x) + a Where "a" is a value that can...

Is this identity true? Identity: \frac{d}{dx} x^n = \lim_{h \rightarrow 0} \frac{(x + h)^n - x^n}{h} = nx^{n-1}

I was wondering if anyone had any links that could show me some Leibniz theroems or maybe a bio. Also, I was wondering, since I don't really know to much about Leibniz Calculus, what would be some major distinctions between Newton's and Leibniz's Calculus, if there are any? And what would...

I'm a bit confused by the leibniz notation for the derivative ie. dy/dx. I've been told that the symbol is not a fraction and can't be split, but I've also seen it split for differentials and the chain rule. Can someone concisely explain what all of it means?

The Leibniz rule: 1. Let f(x,y) be a continuous two variable real function defined on (closed intervals) {x0, x1} x {y0, y1}. 2. Let f_1 (partial derivative of f with respect to the first variable) exists and be continuous on the same subset of RxR. 3. Let F be defined as F(x) = (int) (lim...

need to prove this \frac{\urcorner P \equiv false}{P \equiv true} here is what I did using Leibniz \frac{X \equiv Y}{E[z:=X] \equiv E[z:=Y]} X=\urcorner P Y=false E:\urcorner z z=z \frac{\urcorner P \equiv false}{\urcorner\urcorner P \equiv...

Leibniz integral rule "proof"? Does anyone know how to get the Leibniz integral rule (a.k.a. differentiation under the integral sign)? I'm clueless. It can be found here http://mathworld.wolfram.com/LeibnizIntegralRule.html