The derivative of the function f(x) = 2x/x - 1 is f'(x) = 2/[(x - 1)^2]
How to determine the derivative of the function f(x)?
The function is given as:
f(x) = 2x/x - 1
Next, we make use of the following quotient rule
f'(x) = [VU' - UV']/V^2
Where
U = 2x
V = x - 1
This means that:
U' = 2
V' = 1
V = (x - 1)^2
Substitute these values in the quotient rule equation
f'(x) = [(x - 1) * 2 - 2x * 1]/[(x - 1)^2]
Evaluate the products
f'(x) = [2x - 2 - 2x]/[(x - 1)^2]
Evaluate the like terms
f'(x) = 2/[(x - 1)^2]
Hence, the derivative of the function f(x) = 2x/x - 1 is f'(x) = 2/[(x - 1)^2]
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