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)}

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})

\int \frac{t}{e ^{3 t}} d t

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

a re a 2 x^{2} - 4, x^{2}

d er i v a t i v e f (x) = (x - x^{2})

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)}