What is the derivative of 1/(2x)-5/(3x^2) ?

The derivative of 1/(2x)-5/(3x^2) is -1/(2x^2)+(10)/(3x^3)

What is the first derivative of 1/(2x)-5/(3x^2) ?

The first derivative of 1/(2x)-5/(3x^2) is -1/(2x^2)+(10)/(3x^3)

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derivative

- \frac{1}{2 x ^{2}} + \frac{10}{3 x ^{3}}

Solution steps

\frac{d}{d x} (\frac{1}{2 x} - \frac{5}{3 x ^{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1}{2 x}) - \frac{d}{d x} (\frac{5}{3 x ^{2}})

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

\frac{d}{d x} (\frac{5}{3 x ^{2}}) = - \frac{10}{3 x ^{3}}

= - \frac{1}{2 x ^{2}} - (- \frac{10}{3 x ^{3}})

Simplify

= - \frac{1}{2 x ^{2}} + \frac{10}{3 x ^{3}}

What is the derivative of 1/(2x)-5/(3x^2) ?
The derivative of 1/(2x)-5/(3x^2) is -1/(2x^2)+(10)/(3x^3)
What is the first derivative of 1/(2x)-5/(3x^2) ?
The first derivative of 1/(2x)-5/(3x^2) is -1/(2x^2)+(10)/(3x^3)