F(x)=√x+x^2+1/x-1производную функцию

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вопрос

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