Chain rule Product rule Derivative

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SUMMARY

The discussion focuses on differentiating the expression (2x^2 - 3x + 1)(4x^3 + 4x - 3)^5 using the product rule and chain rule. The product rule formula, a * db/dx + da/dx * b, is applied, where a = (2x^2 - 3x + 1) and b = (4x^3 + 4x - 3)^5. The differentiation of b is further simplified by substituting u = (4x^3 + 4x - 3), leading to db/dx = 5u^4 * du/dx. This structured approach provides a clear method for tackling complex derivatives involving products and compositions of functions.

PREREQUISITES
  • Understanding of the Product Rule in calculus
  • Familiarity with the Chain Rule in calculus
  • Basic knowledge of polynomial differentiation
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Practice differentiating complex polynomials using the Product Rule
  • Study the Chain Rule in greater depth with examples
  • Explore higher-order derivatives and their applications
  • Learn about implicit differentiation for more advanced problems
USEFUL FOR

Students studying calculus, particularly those learning about differentiation techniques, as well as educators looking for examples to illustrate the Product and Chain Rules.

cj123
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Homework Statement



(2x^2 - 3x + 1)(4x^3 + 4x -3)^5

Homework Equations





The Attempt at a Solution

 
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cj123 said:

The Attempt at a Solution


You might need to try this first





Do you know how differentiate single terms,products or quotients?
 
No, I have no problems like this in my notes. We have no textbook to refer back to.
 
Hint:
Topics covered:
Chain rule
Product rule
 
thanks for assisting, but I have no idea where to start on this type of problem.
 
ok I will put it in simple form:

(2x^2 - 3x + 1)(4x^3 + 4x -3)^5
a = (2x^2 - 3x + 1) b = (4x^3 + 4x -3)^5
so a*b

using product rule

a*db/dx + da/dx*b

and now
as b = (4x^3 + 4x -3)^5
make this b = (u)^5
so . db/dx = 5u^4.du/dx ...
 

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