To find the derivative of the function F(x) = √x + x^2 + 1/x - 1, we need to differentiate each term separately using the rules of differentiation.
Differentiate √xThe derivative of √x is (1/2) * x^(-1/2)
Differentiate x^2The derivative of x^2 is 2x
Differentiate 1/xThe derivative of 1/x is -1/x^2
Differentiate the constant term -1The derivative of a constant term is zero.
Now, putting it all together, the derivative of F(x) isF'(x) = (1/2) * x^(-1/2) + 2x - 1/x^2
Simplified, the derivative isF'(x) = 1/(2√x) + 2x - 1/x^2
To find the derivative of the function F(x) = √x + x^2 + 1/x - 1, we need to differentiate each term separately using the rules of differentiation.
Differentiate √x
The derivative of √x is (1/2) * x^(-1/2)
Differentiate x^2
The derivative of x^2 is 2x
Differentiate 1/x
The derivative of 1/x is -1/x^2
Differentiate the constant term -1
The derivative of a constant term is zero.
Now, putting it all together, the derivative of F(x) is
F'(x) = (1/2) * x^(-1/2) + 2x - 1/x^2
Simplified, the derivative is
F'(x) = 1/(2√x) + 2x - 1/x^2