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sml92
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Find the derivative of:
a) y= 2x
---
1-x^2
AND
b) y= x^4-2x+1
----------
(root of) x
a) y= 2x
---
1-x^2
AND
b) y= x^4-2x+1
----------
(root of) x
What are the Derivatives of 2x/(1-x^2) and (x^4-2x+1)/(x^(1/2))?
- Thread starter sml92
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SUMMARY
The derivatives of the functions provided in the discussion are calculated using specific calculus rules. For the function y = 2x/(1-x^2), the quotient rule is applied, resulting in the derivative y' = (2(1-x^2) - 2x(-2x))/(1-x^2)^2. For the function y = (x^4 - 2x + 1)/√x, the expression is simplified using the power rule with fractional exponents, yielding the derivative y' = (4x^3 - 2)/(2x^(3/2)). Both methods demonstrate the application of fundamental calculus techniques.
PREREQUISITES- Understanding of the Quotient Rule in calculus
- Familiarity with the Power Rule and fractional exponents
- Basic knowledge of derivatives and their notation
- Ability to manipulate algebraic expressions
- Practice applying the Quotient Rule on various rational functions
- Explore the Power Rule with fractional exponents in more complex scenarios
- Learn about implicit differentiation for functions not easily expressed in standard form
- Study higher-order derivatives and their applications in physics and engineering
Students studying calculus, mathematics educators, and anyone looking to strengthen their understanding of derivative calculations and rules.