F(x) =(5 -2√x)/(2√x -1) , x(0) =4.
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f '(x(0)) = f '(4) -?
f '(x) =((5 -2√x)/(2√x -1)) ' = (5 -2√x)' *(2√x -1) -(5 -2√x)*(2√x -1) ' / (2√x -1)² =
(0 -1/√x)*(2√x -1) - (5 -2√x)*(1/√x -0) / (2√x -1)² =
((-1/√x)*(2√x -1) - (1/√x)*(5-2√x)) / (2√x -1)² = (-1/√x)*(2√x -1+5 -2√x) / (2√x -1)²
= -4/(√x( (2√x -1)² ).
f '(4) = -4/(√4*(2√4 -1)²) = -4/(2*(4 -1)² = - 2/9.
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* * * f(x) =(5 -2√x)/(2√x -1) =(4 -(2√x -1))/(2√x -1) =4/((2√x -1) -1. * * *
f '(x) =((4/((2√x -1) -1)' = (4*((2√x -1)^(-1)) ' -1 ' = - 4*(2√x -1)^(-2)*(2√x -1)' -0 =
-4/(2√x -1)²*((2√x)' -1') =-4/(√x(2√x -1)² ).
f '(4) = -4/(√4*(2√4 -1)²) = -4/(2*(4 -1)² = - 2/9.