What is the derivative of (x^3/6+1/(2x)) ?

The derivative of (x^3/6+1/(2x)) is (x^2)/2-1/(2x^2)

What is the first derivative of (x^3/6+1/(2x)) ?

The first derivative of (x^3/6+1/(2x)) is (x^2)/2-1/(2x^2)

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\frac{d}{d x} (\frac{x ^{3}}{6} + \frac{1}{2 x})

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

Solution steps

\frac{d}{d x} (\frac{x ^{3}}{6} + \frac{1}{2 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{3}}{6}) + \frac{d}{d x} (\frac{1}{2 x})

\frac{d}{d x} (\frac{x ^{3}}{6}) = \frac{x ^{2}}{2}

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

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

What is the derivative of (x^3/6+1/(2x)) ?
The derivative of (x^3/6+1/(2x)) is (x^2)/2-1/(2x^2)
What is the first derivative of (x^3/6+1/(2x)) ?
The first derivative of (x^3/6+1/(2x)) is (x^2)/2-1/(2x^2)