Derivatives and order of operations/rules

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SUMMARY

The discussion focuses on the application of the chain rule and product rule in calculus, specifically in differentiating complex functions. An example provided is the differentiation of the function y = (2x+1)^5 * (x^3-x+1)^4, which requires the use of both rules. Key reminders include that the derivative of a sum is the sum of the derivatives and that constants multiply the derivative of the function. The importance of correctly identifying when to apply each rule is emphasized for accurate differentiation.

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  • Understanding of basic calculus concepts, including derivatives
  • Familiarity with the chain rule and product rule
  • Knowledge of power rule for differentiation
  • Ability to manipulate algebraic expressions
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  • Practice differentiating functions using the chain rule and product rule
  • Study examples of complex derivatives involving multiple rules
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Students studying calculus, mathematics educators, and anyone looking to strengthen their understanding of differentiation techniques.

Aznclink
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Hi, I am having troubles with derivitives like should i use chain rule first before using product rule and such.

heres an example problem:

3(1-5x)^1/2 + 1/6(1-5x)^3/2

What should my following steps be?
 
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Welcome to Physicsforums aznclink.

Remember that the derivative of a sum is the sum of the derivatives, the derivative of c f(x) is c times the derivative of f(x) when c is a constant, the power rule and to use the chain rule when finding the derivative of (1-5x)^(1/2) etc.

Hope that helps!
 
Last edited:
aznclink, the following example is one where you have to use both chain and product rule:
differentiate: y = (2x+1)^5 * (x^3-x+1)^4.
In this example you must first use the product rule, y=f(x)g'(x) + g(x)f'(x), and then the chain rule to find g'(x) and f'(x).

hope this helps.
 

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