The discussion revolves around the application of the product rule in calculus, specifically in the context of differentiating the expression 112 - xln(x^3). Participants are exploring when to appropriately apply the product rule versus other differentiation techniques.
The conversation is ongoing, with participants providing insights and clarifications regarding the use of the product rule and the chain rule. There is recognition of different interpretations of the expression, leading to varied applications of the product rule.
Some participants express uncertainty about the derivative of the function and the notation used, which may affect the application of the product rule. There is a noted typo in the discussion that led to some confusion regarding terminology.
939 said: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)
Don't you mean the product rule? g(x)h(x) is a product, so the product rule would be applicable.mjordan2nd said: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
mjordan2nd said: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.