Applying terms in square roots -yeesh

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SUMMARY

The discussion focuses on applying the chain rule to differentiate functions involving square roots, specifically the function f(x) = √(ax + b). The user expresses difficulty in computing the derivative at a specific point, f'(6). The solution involves substituting u = ax + b and applying the chain rule, which is essential for correctly differentiating composite functions. Understanding this method is crucial for solving similar problems in calculus.

PREREQUISITES
  • Understanding of basic calculus concepts, particularly differentiation.
  • Familiarity with the chain rule in calculus.
  • Knowledge of square root functions and their properties.
  • Ability to manipulate algebraic expressions involving variables.
NEXT STEPS
  • Study the application of the chain rule in various contexts.
  • Practice differentiating functions involving square roots using examples.
  • Learn about implicit differentiation for more complex functions.
  • Explore advanced calculus topics such as higher-order derivatives.
USEFUL FOR

Students studying calculus, educators teaching differentiation techniques, and anyone needing to apply the chain rule in mathematical problems involving square roots.

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http://img522.imageshack.us/img522/7522/mat4vj.gif where X is the number into the term http://img524.imageshack.us/img524/2985/prob23ei.gif
Computer F'(6)

The square root is what's giving me my most difficulty. I don't know how to apply the term with a square root and computer f'(6). I've about given up, but it's important to know. Help is needed for this one.
 
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Do you know the chain rule?

Think of the general case where [itex]f(x) = \sqrt{ax + b} = (ax+b)^{0.5}[/itex]. Now let u=ax+b and apply the chain rule.
 

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