What is the derivative of 1/2 x^2+x^{-1} ?

The derivative of 1/2 x^2+x^{-1} is x-1/(x^2)

What is the first derivative of 1/2 x^2+x^{-1} ?

The first derivative of 1/2 x^2+x^{-1} is x-1/(x^2)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

\int x^{2} - 4 x d x

\int_{1}^{3} 3 r^{3} ln (r) d r

\int (7 x - 11)^{4} d x

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 t^{3}

\frac{d}{d x} (ln (x^{4} - 6 x^{2}))

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