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

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

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

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

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

\frac{3 x ^{2}}{2} - \frac{1}{6 x ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{3 x ^{2}}{2} - \frac{1}{6 x ^{2}}

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