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If y = x then dy, the differential of y, as a changes from 64 to 64.1 is given
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Answer:


dy \ = \ 0.1

Explanation:

Considering the Leibniz notation to represent the derivative of
y with respect to
x, suppose
y \ = \ f\left(x\right) is a differentiable function, let
dx be the independent variable such that it can be designated with any nonzero real number, and define the dependent variable
dy as


dy \ = \ f'\left(x\right) \ dx,

where
dy is the function of both
x and
dx. Hence, the terms
dy and
dx are known as differentials

Dividing both sides of the equation by
dy, yield the familiar expression


\displaystyle(dy)/(dx) \ = \ f'\left(x\right).

Given that
f\left(x\right) \ = \ x and
dx \ = \ 64.1 \ - \ 64 \ = \ 0.1, hence


f'\left(x\right) \ = \ 1.

Subsequently,


dy \ = \ f'\left(64\right) \ * \ 0.1 \\ \\ dy \ = \ 1 \ * \ 0.1 \\ \\ dy \ = \ 0.1.

User Juanjo Rodriguez
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