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182075
18.02.2021 •
Mathematics
F(x)= y-x/x^2-16
(that’s a fraction; and the ^ indicates the 2 is a exponent)
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Ответ:
= 1/x^2
Step-by-step explanation:
Possible derivation:
d/dx(-16 - 1/x + y)
Differentiate the sum term by term and factor out constants:
= d/dx(-16) - d/dx(1/x) + d/dx(y)
The derivative of -16 is zero:
= -(d/dx(1/x)) + d/dx(y) + 0
Simplify the expression:
= -(d/dx(1/x)) + d/dx(y)
Use the power rule, d/dx(x^n) = n x^(n - 1), where n = -1.
d/dx(1/x) = d/dx(x^(-1)) = -x^(-2):
= d/dx(y) - -1/x^2
Simplify the expression:
= 1/x^2 + d/dx(y)
The derivative of y is zero:
= 1/x^2 + 0
Simplify the expression:
= 1/x^2
Ответ: