The discussion focuses on differentiating the function (1-2x3+x2)((1/x3)+1) using the product rule. The correct application of the product rule is f'g(x) + g'f(x), where f'(x) = -6x3 + 2x and g'(x) = -1/x4. The participant encountered errors in calculating g'(x) and f'(x)g(x), highlighting the importance of accurate differentiation in calculus.
PREREQUISITESStudents studying calculus, particularly those learning about differentiation techniques, and educators seeking to clarify common errors in applying the product rule.
Your result for g'(x) is wrong, assuming that g(x)=1/x3+1. Your f'(x)g(x) is wrong too.digidako said:Homework Statement
(1-2x3+x2)((1/x3)+1)
Homework Equations
f'g(x)+g'f(x)
f'(x)=-6x3+2x
g'(x)=(-1/x4)
The Attempt at a Solution
I found what i believe to be the derivative of both f(x) & g(x) and used the product rule to get to where I am stuck right now:
[(-6x2+2x)(1/x3)]+[(-1/x4)(1-2x3+x2)