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

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

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

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

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derivative of

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

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

Solution steps

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

Simplify

\frac{1}{6} x^{3} + \frac{1}{2 x} : \frac{x ^{3}}{6} + \frac{1}{2 x}

= \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}}

\frac{d}{d x} (4 + 3 f (x))

x \to 0 + lim (ln (\frac{9}{x ^{3}}))

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

e^{4 t}

x \to 0 lim ((\frac{2}{x})^{x})

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