No.939 said:Homework Statement
Let μ represent a positive constant.
Find the derivatives of:
(x^2)/(2μ)
Please check work. I am confused about the "constant" part. Can't you just set μ = some positive number and find the derivative that way?
The second 2μ factor in the numerator is wrong. μ is a constant, so 2μ is also a constant. The derivative of any constant is zero.939 said:Homework Equations
(x^2)/(2μ)
The Attempt at a Solution
((2x)(2μ) - (x^2)(2μ))/(2μ)^2
No one should use the product or quotient rule on problems of this type. If they do, it's because they don't know better.1MileCrash said:I just want to add that no one would ever use the product or quotient rule to do this.
Not weird, IMO, just a lack of experience.eumyang said:Perhaps, but I have seen students who do, however, use a quotient rule even if the denominator is a constant. Weird, for sure... (shrugs)
Derivatives with constants refer to the process of finding the rate of change of a function that contains a fixed number or value. In other words, it is the derivative of a function where a constant is added or multiplied to the variable.
The derivative of a constant is always 0, as a constant value does not change. This means that when taking the derivative of a function with a constant, the constant can be ignored and the derivative of the remaining variable can be found.
The main difference between the two is that a derivative with a constant will result in a constant value, while a derivative without a constant will result in a variable or function. Additionally, a derivative with a constant will have a slope of 0, while a derivative without a constant will have a varying slope.
A constant will not change the overall shape of a graph when taking the derivative. However, it may affect the y-intercept or the steepness of the slope, depending on how it is used in the function.
Yes, a constant can be a variable in a derivative. This is often seen in situations where a constant is used to represent a specific value or parameter, such as in physics equations. In this case, the constant can be treated as a variable and its derivative can be found.