Chain rule Product rule Derivative

AI Thread Summary
To differentiate the expression (2x^2 - 3x + 1)(4x^3 + 4x - 3)^5, the product rule and chain rule are essential. The product rule states that the derivative of a product of two functions is the first function times the derivative of the second plus the second function times the derivative of the first. For the second function, (4x^3 + 4x - 3)^5, the chain rule is applied by letting u = (4x^3 + 4x - 3), leading to the derivative db/dx = 5u^4(du/dx). This approach allows for systematic differentiation of complex polynomial expressions. Understanding these rules is crucial for solving similar calculus problems effectively.
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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