What is the derivative of 1/(sqrt(3x)) ?

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

What is the first derivative of 1/(sqrt(3x)) ?

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

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derivative of

\frac{1}{3 x}

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 4 lim (\frac{x + 4}{x - 4})

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\int 3 e^{- 4 x} sin (e^{- 4 x}) d x

x \to 3 lim ([8 (- 10)])

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