- #1
UMath1
- 361
- 9
Why wouldn't this work?
UMath1 said:I understand that I put in an extra Δx. But how is Δ(g(x)h(x)) beung computed incorrectly?
I agree completely. The image you posted in #3 can be done right here in the text input pane.Orodruin said:Also, you should stop attaching images like these. They are going to be impossible to read on most mobile devices and impossible to quote properly. There is a tutorial on how to write proper forum maths here: https://www.physicsforums.com/help/latexhelp/
The product rule proof is a mathematical formula used in calculus to find the derivative of two functions multiplied together. It is important in science because it allows us to calculate the rate of change of a product of two variables, which is crucial in many scientific fields such as physics, chemistry, and engineering.
To prove the product rule, we start by defining a function f(x) as the product of two functions, g(x) and h(x). We then use the definition of the derivative to expand f'(x) and simplify it to get the product rule formula, which is (g(x)*h'(x))+(h(x)*g'(x)).
Some common mistakes when using the product rule include forgetting to add the second term in the formula (+h(x)*g'(x)), making errors in simplifying the expanded derivative, and incorrectly identifying which function is g(x) and which is h(x).
Yes, the product rule can be extended to any number of functions multiplied together. The general formula for n functions is (f1' * f2 * f3 * ... * fn) + (f1 * f2' * f3 * ... * fn) + ... + (f1 * f2 * f3 * ... * fn').
Yes, there are alternative methods such as the quotient rule, chain rule, and power rule, which can be used to find the derivative of a product of functions. The choice of method depends on the complexity of the functions involved and personal preference.