What is the derivative of 2/(3sqrt(x)) ?

The derivative of 2/(3sqrt(x)) is -1/(3x^{3/2)}

What is the first derivative of 2/(3sqrt(x)) ?

The first derivative of 2/(3sqrt(x)) is -1/(3x^{3/2)}

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

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

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

Simplify

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

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

y^{^{'''}} - 2 y^{^{'}} + y = 0

\int - 9 sin (3 x) d x

\int 12 x ln (3 x) d x

\frac{d y}{d t} = t y^{\frac{1}{3}}

2 + e^{2 t} + e^{- 2 t}

What is the derivative of 2/(3sqrt(x)) ?
The derivative of 2/(3sqrt(x)) is -1/(3x^{3/2)}
What is the first derivative of 2/(3sqrt(x)) ?
The first derivative of 2/(3sqrt(x)) is -1/(3x^{3/2)}