U substitution for differentiation?

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SUMMARY

The discussion focuses on using U substitution for differentiation, specifically evaluating the derivative of the function sqrt(t^4 + t^2) to find maximum or minimum values. The user successfully applies the chain rule by letting u = t^4 + t^2, leading to the derivative expression d(sqrt(u))/dt = (1/2)u^(-1/2) * (4t^3 + 2t). This method effectively simplifies the differentiation process and aids in identifying critical points for optimization.

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  • Understanding of basic calculus concepts, particularly differentiation
  • Familiarity with the chain rule in calculus
  • Knowledge of U substitution techniques in differentiation
  • Ability to manipulate algebraic expressions involving exponents
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  • Study the application of the chain rule in more complex functions
  • Explore optimization techniques in calculus, focusing on critical points
  • Learn about implicit differentiation and its applications
  • Investigate the use of U substitution in integration for further mathematical insights
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Students and professionals in mathematics, particularly those studying calculus, as well as educators looking for effective methods to teach differentiation techniques.

kurious
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How do I evaluate:

d/dt sqrt [ t^4 + t^2 ]= 0
to get a max/min value.

can I make a u substitution of some sort?
 
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Yes, that's basically just the "chain rule".

Let u= t4+ t2

then d sqrt(t4+ t2)/dt= d u1/2/du* du/dt
= (1/2)u-1/2 * (4t3+ 2t)
= (1/2)(t4+t2)-1/2)*(4t3+ 2t)
 
Thanks for your help.
 

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