What is the derivative of f(x)=x+1/x ?

The derivative of f(x)=x+1/x is 1-1/(x^2)

What is the first derivative of f(x)=x+1/x ?

The first derivative of f(x)=x+1/x is 1-1/(x^2)

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derivative

1 - \frac{1}{x ^{2}}

Solution steps

\frac{d}{d x} (x + \frac{1}{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d x}{d x} + \frac{d}{d x} (\frac{1}{x})

\frac{d x}{d x} = 1

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

= 1 - \frac{1}{x ^{2}}

What is the derivative of f(x)=x+1/x ?
The derivative of f(x)=x+1/x is 1-1/(x^2)
What is the first derivative of f(x)=x+1/x ?
The first derivative of f(x)=x+1/x is 1-1/(x^2)