Product Rule in Derivatives: When to Use and When to Avoid

[939]

Homework Statement

In this equation, how do you know when you would use the product rule for the second part, and when you wouldn't?

Homework Equations

112 - xlnx^3

The Attempt at a Solution

I.e. with product rule
(-1)(lnx^3) + (-x)((3)(1/x)
or without?
(-3x)(1/x)

 

[mjordan2nd]

If you want to find the derivative of a function f(x) that can be written as g(x)h(x) you need to use the product rule unless you know the derivative of f directly. You don't know the derivative of f(x) directly (at least I don't), but you should be able to calculate the derivative of both g(x) and h(x). However, you should note that for the natural log part, if I'm interpreting your notation correctly, you need to use the chain rule as well to find the derivative.

 

[Dick]

Homework Statement

In this equation, how do you know when you would use the product rule for the second part, and when you wouldn't?

Homework Equations

112 - xlnx^3

The Attempt at a Solution

I.e. with product rule
(-1)(lnx^3) + (-x)((3)(1/x)
or without?
(-3x)(1/x)

The answer depends on whether you mean x*ln(x^3) or x*(ln(x))^3. You use the product rule either way. The answers are different. But you still use the product rule.

 

[Mark44]

If you want to find the derivative of a function f(x) that can be written as g(x)h(x) you need to use the power rule

Don't you mean the product rule? g(x)h(x) is a product, so the product rule would be applicable.

unless you know the derivative of f directly. You don't know the derivative of f(x) directly (at least I don't), but you should be able to calculate the derivative of both g(x) and h(x). However, you should note that for the natural log part, if I'm interpreting your notation correctly, you need to use the chain rule as well to find the derivative.

 

[mjordan2nd]

Absolutely, thanks for catching that. Typo on my part.