Derivative of a Polynomial Function?

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SUMMARY

The derivative of the polynomial function f(x) = (x^2 + 3x - 2)(x^3 - 4) is confirmed to be f'(x) = 5x^4 + 12x^3 - 6x^2 - 8x - 12. The product rule is essential for this calculation, as it involves differentiating each component of the function. The correct application of the product rule is demonstrated as follows: f'(x) = (x^2 + 3x - 2)'(x^3 - 4) + (x^2 + 3x - 2)(x^3 - 4)'.

PREREQUISITES
  • Understanding of polynomial functions
  • Knowledge of the product rule in calculus
  • Familiarity with differentiation techniques
  • Ability to perform polynomial multiplication
NEXT STEPS
  • Study the product rule in detail
  • Practice differentiating more complex polynomial functions
  • Learn about the chain rule and its applications
  • Explore graphical representations of polynomial derivatives
USEFUL FOR

Students studying calculus, particularly those focusing on differentiation techniques, as well as educators looking for examples of polynomial derivatives.

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Homework Statement



Find derivative of function?
if f(x) = (x^2 + 3x -2 ) (x^3-4)
Find f`(x)

Homework Equations



FOIL or Multiply both

The Attempt at a Solution



I get
5x^4 + 12x^3 - 6x^2 -8x-12

is this right?
 
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Yes, it's correct. Why do you think it might not be??
 
just checking
 
I'd use the product rule.
 
10min said:

Homework Statement



Find derivative of function?
if f(x) = (x^2 + 3x -2 ) (x^3-4)
Find f`(x)

Homework Equations



FOIL or Multiply both

The Attempt at a Solution



I get
5x^4 + 12x^3 - 6x^2 -8x-12

is this right?

yes i believe it is.
 
You could check by using the product rule as ducnguyen2000 suggested:
the derivative of f(x) = (x^2 + 3x -2 ) (x^3-4) is (x^2+ 3x- 2)'(x^3- 4)+ (x^2+ 3x- 2)(x^3- 4)'.
 

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