What is the derivative of f(x)= 2/(3x)-1/(6sqrt(x)) ?

The derivative of f(x)= 2/(3x)-1/(6sqrt(x)) is (-8x^{3/2}+x^2)/(12x^{7/2)}

What is the first derivative of f(x)= 2/(3x)-1/(6sqrt(x)) ?

The first derivative of f(x)= 2/(3x)-1/(6sqrt(x)) is (-8x^{3/2}+x^2)/(12x^{7/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

f (x) = \frac{2}{3 x} - \frac{1}{6 x}

\frac{- 8 x ^{\frac{3}{2}} + x ^{2}}{12 x ^{\frac{7}{2}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (\frac{1}{6 x}) = - \frac{1}{12 x ^{\frac{3}{2}}}

= - \frac{2}{3 x ^{2}} - (- \frac{1}{12 x ^{\frac{3}{2}}})

Simplify

- \frac{2}{3 x ^{2}} - (- \frac{1}{12 x ^{\frac{3}{2}}}) : \frac{- 8 x ^{\frac{3}{2}} + x ^{2}}{12 x ^{\frac{7}{2}}}

= \frac{- 8 x ^{\frac{3}{2}} + x ^{2}}{12 x ^{\frac{7}{2}}}

What is the derivative of f(x)= 2/(3x)-1/(6sqrt(x)) ?
The derivative of f(x)= 2/(3x)-1/(6sqrt(x)) is (-8x^{3/2}+x^2)/(12x^{7/2)}
What is the first derivative of f(x)= 2/(3x)-1/(6sqrt(x)) ?
The first derivative of f(x)= 2/(3x)-1/(6sqrt(x)) is (-8x^{3/2}+x^2)/(12x^{7/2)}