Answer:
= -2/x^3
Explanation:
Possible derivation:
d/dx(d/dx((x^2 + 2 x - 1)/x))
Distribute 1/x through x^2 + 2 x - 1:
= d/dx((d/dx(2 - 1/x + x)))
Differentiate the sum term by term and factor out constants:
= d/dx((d/dx(2) - d/dx(1/x) + d/dx(x)))
The derivative of 2 is zero:
= d/dx(0 - d/dx(1/x) + d/dx(x))
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(0 - -1/x^2 + d/dx(x))
The derivative of x is 1:
= d/dx(0 - -1/x^2 + 1)
Differentiate the sum term by term:
= d/dx(1) + d/dx(1/x^2)
The derivative of 1 is zero:
= d/dx(1/x^2) + 0
Simplify the expression:
= d/dx(1/x^2)
Use the power rule, d/dx(x^n) = n x^(n - 1), where n = -2.
d/dx(1/x^2) = d/dx(x^(-2)) = -2 x^(-3):
Answer: = -2/x^3