What is the derivative of f(x)=-x+4/x+1 ?

The derivative of f(x)=-x+4/x+1 is -4/(x^2)-1

What is the first derivative of f(x)=-x+4/x+1 ?

The first derivative of f(x)=-x+4/x+1 is -4/(x^2)-1

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derivative of

f (x) = - x + \frac{4}{x} + 1

- \frac{4}{x ^{2}} - 1

Solution steps

\frac{d}{d x} (- x + \frac{4}{x} + 1)

Apply the Sum/Difference Rule:

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

= - \frac{d x}{d x} + \frac{d}{d x} (\frac{4}{x}) + \frac{d}{d x} (1)

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

\frac{d}{d x} (\frac{4}{x}) = - \frac{4}{x ^{2}}

\frac{d}{d x} (1) = 0

= - 1 - \frac{4}{x ^{2}} + 0

Simplify

= - \frac{4}{x ^{2}} - 1

What is the derivative of f(x)=-x+4/x+1 ?
The derivative of f(x)=-x+4/x+1 is -4/(x^2)-1
What is the first derivative of f(x)=-x+4/x+1 ?
The first derivative of f(x)=-x+4/x+1 is -4/(x^2)-1