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Sagot :
Answer:
[tex]dy \ = \ 0.1[/tex]
Step-by-step explanation:
Considering the Leibniz notation to represent the derivative of [tex]y[/tex] with respect to [tex]x[/tex], suppose [tex]y \ = \ f\left(x\right)[/tex] is a differentiable function, let [tex]dx[/tex] be the independent variable such that it can be designated with any nonzero real number, and define the dependent variable [tex]dy[/tex] as
[tex]dy \ = \ f'\left(x\right) \ dx[/tex],
where [tex]dy[/tex] is the function of both [tex]x[/tex] and [tex]dx[/tex]. Hence, the terms [tex]dy[/tex] and [tex]dx[/tex] are known as differentials
Dividing both sides of the equation by [tex]dy[/tex], yield the familiar expression
[tex]\displaystyle\frac{dy}{dx} \ = \ f'\left(x\right)[/tex].
Given that [tex]f\left(x\right) \ = \ x[/tex] and [tex]dx \ = \ 64.1 \ - \ 64 \ = \ 0.1[/tex], hence
[tex]f'\left(x\right) \ = \ 1[/tex].
Subsequently,
[tex]dy \ = \ f'\left(64\right) \ \times \ 0.1 \\ \\ dy \ = \ 1 \ \times \ 0.1 \\ \\ dy \ = \ 0.1[/tex].
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