What is the derivative of 1/(sqrt(6x)) ?

The derivative of 1/(sqrt(6x)) is -1/(2sqrt(6)x^{3/2)}

What is the first derivative of 1/(sqrt(6x)) ?

The first derivative of 1/(sqrt(6x)) is -1/(2sqrt(6)x^{3/2)}

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derivative of

\frac{1}{6 x}

- \frac{1}{2 6 x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{6 x})

Apply exponent rule:

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

= \frac{d}{d x} ((6 x)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 6 x ) ^{\frac{3}{2}}} \frac{d}{d x} (6 x)

= - \frac{1}{2 ( 6 x ) ^{\frac{3}{2}}} \frac{d}{d x} (6 x)

\frac{d}{d x} (6 x) = 6

= - \frac{1}{2 ( 6 x ) ^{\frac{3}{2}}} \cdot 6

Simplify

- \frac{1}{2 ( 6 x ) ^{\frac{3}{2}}} \cdot 6 : - \frac{1}{2 6 x ^{\frac{3}{2}}}

= - \frac{1}{2 6 x ^{\frac{3}{2}}}

\int e^{t y} (4 y + 1) d y

\int e^{2 x} \cdot sin (x) d x

f (x) = \frac{1}{6} x^{4}, at x = - 1

1 - e^{- t} sin (2 t)

\frac{d}{d x} (8 x (x^{2} + 3)^{3})

What is the derivative of 1/(sqrt(6x)) ?
The derivative of 1/(sqrt(6x)) is -1/(2sqrt(6)x^{3/2)}
What is the first derivative of 1/(sqrt(6x)) ?
The first derivative of 1/(sqrt(6x)) is -1/(2sqrt(6)x^{3/2)}