Derivative of square roots and composition functions

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SUMMARY

The discussion focuses on taking the derivative of the function defined as the square root of a composition of functions, specifically sqr(4 + sqr(3x)). The user correctly identifies the need to apply the chain rule and separates the function into F(x) = (4 + x)^(1/2) and G(x) = (3x)^(1/2). To find the derivative, one must first apply the power rule to F(x) and then differentiate the inner function accordingly, ensuring to utilize the chain rule effectively.

PREREQUISITES
  • Understanding of the chain rule in calculus
  • Familiarity with the power rule for differentiation
  • Knowledge of composition functions
  • Basic algebraic manipulation skills
NEXT STEPS
  • Review the chain rule for derivatives in calculus
  • Practice the power rule with various functions
  • Explore composition functions and their derivatives
  • Study examples of derivatives involving square root functions
USEFUL FOR

Students learning calculus, particularly those focusing on differentiation techniques, as well as educators seeking to clarify the application of the chain rule and power rule in derivative calculations.

tmoney369
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how do i take the derivative of sqr(4 + sqr(3x))?
My teacher wants me to do it as a chain rule composition function so i separated it into

F(x)= (4+x)^1/2 and G(x)= (3x)^1/2

but i don't know where to go from here because i don't know how to take the derivative of f(x)
 
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on F(x) you must use the power rule then go inside your function and take the derivative
 

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