Answer :
Final answer:
To find the differentials of the given functions, we can use the rules of differentiation. The differentials for the functions are:
[tex]1. dy = 12x^3 + 2x - 2, 2. dy[/tex][tex]1/2)(1 + x)^(-1/2), and 4. dy = (2x - x^2 - 2)/(x - 1)^2.[/tex]Explanation:
To find the differentials of the given functions, we can use the rules of differentiation. Let's find the differentials for each function:
- y = 3x4 + x2 - 2x + 1 (Differential: dy = 12x3 + 2x - 2)
- y = xcos(x) (Differential: dy = cos(x) - xsin(x))
- y = sqrt(1 + x) (Differential: dy = (1/2)(1 + x)-1/2)
- y = (x2 + 2)/(x - 1) (Differential: dy = (2x - x2 - 2)/(x - 1)2)
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