- #1
edgepflow
- 688
- 1
d/dx [ (1/y) dy/dx) ] = ?
Please let me know !
Please let me know !
armolinasf said:Are you just asking what the derivative of 1/y is with respect to x? If that's the case you should give it a try first using implicit differentiation.
Thanks DyslexicHobo. That link is what I needed!DyslexicHobo said:I haven't taken calculus in quite some time, but this is the resource I use for all of the calculus that I've forgotten:
www.wolframalpha.com
It's EXTREMELY easy to use. So easy that all I needed to do was copy and paste straight from your post. The great thing is that for most problems, you can even click "Show Steps" next to the answer and it'll walk you through the problem. For this problem, you would use the quotient rule. (I'm assuming Y is a function of X... if it's not, then I don't think this solution is correct).
Here is the solution and steps: http://www.wolframalpha.com/input/?i=d/dx+[+%281%2Fy%29+*+%28dy%2Fdx%29+]
A derivative is a mathematical concept that measures the rate of change of a function with respect to its input variable. In simpler terms, it describes how the output of a function changes when the input changes.
Checking a derivative is important because it allows us to verify the accuracy of our calculations and ensure that we have correctly calculated the rate of change of a function. It also allows us to identify and correct any errors.
To check a derivative, we can use various methods such as the limit definition, differentiation rules, and algebraic manipulation. We can also use graphing techniques to visually confirm the accuracy of our derivative.
Derivatives are used in a variety of applications, including optimization problems, finding maximum and minimum values, and determining the slope of a tangent line. They also play a crucial role in physics, engineering, and economics.
Yes, some common mistakes when checking a derivative include forgetting to apply the chain rule, using the wrong differentiation rule, and making algebraic errors. It is also important to check for continuity and differentiability of the function before taking the derivative.