# Homework Help: Derivatives with constants

1. Feb 11, 2014

### 939

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

(x^2)/(2μ)

3. The attempt at a solution

((2x)(2μ) - (x^2)(2μ))/(2μ)^2

2. Feb 11, 2014

### Staff: Mentor

No.
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.

Also, there are at least two other ways to do this problem, both of which are simpler than using the quotient rule.

Dividing by 2μ is the same as multiplying by 1/(2μ), so you can use the product rule, which is usually less prone to algebra mistakes.

You can also use the constant multiple rule. IOW, d/dx(k*f(x)) = k * d/dx(f(x)).

3. Feb 12, 2014

### 1MileCrash

I just want to add that no one would ever use the product or quotient rule to do this.

4. Feb 12, 2014

### eumyang

Perhaps, but I have seen students who do, however, use a quotient rule even if the denominator is a constant. Weird, for sure... (shrugs)

5. Feb 12, 2014

### Staff: Mentor

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.

Not weird, IMO, just a lack of experience.