Simplify derivative after using product and chain rule

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SUMMARY

The discussion focuses on simplifying the derivative of the function (x² - x⁻¹ + 1)(x³ + 2x - 6)⁷ using the product rule and chain rule. The user initially applies the chain rule and power rule correctly but struggles with further simplification, indicating potential errors in subsequent calculations. The community suggests verifying each step for mistakes, particularly with signs, to ensure accuracy in the final result.

PREREQUISITES
  • Understanding of the Product Rule in calculus
  • Familiarity with the Chain Rule in calculus
  • Knowledge of the Power Rule in calculus
  • Ability to simplify algebraic expressions
NEXT STEPS
  • Review the application of the Product Rule in calculus
  • Practice simplifying derivatives using the Chain Rule
  • Explore common mistakes in derivative calculations
  • Study examples of complex derivatives involving multiple rules
USEFUL FOR

Students studying calculus, particularly those learning about differentiation techniques, and anyone seeking to improve their skills in simplifying complex derivatives.

biochem850
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Homework Statement



(x[itex]^{2}[/itex]-x[itex]^{-1}[/itex]+1)(x[itex]^{3}[/itex]+2x-6)[itex]^{7}[/itex]

Homework Equations


Chain Rule & Power Rule

The Attempt at a Solution



(x[itex]^{3}[/itex]+2x-6)[itex]^{6}[/itex][(x[itex]^{3}[/itex]+2x-6)(2x+x[itex]^{-2}[/itex])+7(3x[itex]^{2}[/itex]+2)(x[itex]^{2}[/itex]-x[itex]^{-1}[/itex]+1)]

This is the farthest I've gotten but when I do additional computation I do not arrive at the correct simplified solution.

edit- should be "simplify derivative after using power rule and chain rule"

Homework Statement

Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution

 
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hi biochem850! :wink:

looks ok so far :smile:

you've probably made a mistake with a minus somewhere later …

check them first …

if that doesn't help, then show us what you did​
 

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