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

The derivative of 3/(2sqrt(3x)) is -(sqrt(3))/(4x^{3/2)}

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

The first derivative of 3/(2sqrt(3x)) is -(sqrt(3))/(4x^{3/2)}

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

- \frac{3}{4 x ^{\frac{3}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Simplify

\frac{3}{2} (- \frac{1}{2 ( 3 x ) ^{\frac{3}{2}}} \cdot 3) : - \frac{3}{4 x ^{\frac{3}{2}}}

= - \frac{3}{4 x ^{\frac{3}{2}}}

y = (5)^{x}, at x = 6

x \to - 2 lim (\frac{- 1}{( x + 2 )})

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

\frac{d}{d x} (\frac{1}{5})

\frac{3 - 2 x + 5}{x - 2}

What is the derivative of 3/(2sqrt(3x)) ?
The derivative of 3/(2sqrt(3x)) is -(sqrt(3))/(4x^{3/2)}
What is the first derivative of 3/(2sqrt(3x)) ?
The first derivative of 3/(2sqrt(3x)) is -(sqrt(3))/(4x^{3/2)}