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)}

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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}}}

sin (x), π

\frac{d P}{d t} = P (850 - P)

\frac{d y}{d x} = - y

y^{^{'}} + \frac{5}{x} y = 0

\int_{- \infty}^{0} x e^{x} d x

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)}