Finding Derivatives with Constants

[939]

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?

Homework Equations

(x^2)/(2μ)

The Attempt at a Solution

((2x)(2μ) - (x^2)(2μ))/(2μ)^2

 

[Mark44]

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?

No.

Homework Equations

(x^2)/(2μ)

The Attempt at a Solution

((2x)(2μ) - (x^2)(2μ))/(2μ)^2

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)).

 

[1MileCrash]

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

 

[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)

 

[Mark44]

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

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.

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

Not weird, IMO, just a lack of experience.