What is the derivative of 1/(sqrt(7x)) ?

The derivative of 1/(sqrt(7x)) is -1/(2sqrt(7)x^{3/2)}

What is the first derivative of 1/(sqrt(7x)) ?

The first derivative of 1/(sqrt(7x)) is -1/(2sqrt(7)x^{3/2)}

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\frac{d}{d x} (\frac{1}{7 x})

- \frac{1}{2 7 x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{7 x})

Apply exponent rule:

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

= \frac{d}{d x} ((7 x)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 7 x ) ^{\frac{3}{2}}} \frac{d}{d x} (7 x)

= - \frac{1}{2 ( 7 x ) ^{\frac{3}{2}}} \frac{d}{d x} (7 x)

\frac{d}{d x} (7 x) = 7

= - \frac{1}{2 ( 7 x ) ^{\frac{3}{2}}} \cdot 7

Simplify

- \frac{1}{2 ( 7 x ) ^{\frac{3}{2}}} \cdot 7 : - \frac{1}{2 7 x ^{\frac{3}{2}}}

= - \frac{1}{2 7 x ^{\frac{3}{2}}}

What is the derivative of 1/(sqrt(7x)) ?
The derivative of 1/(sqrt(7x)) is -1/(2sqrt(7)x^{3/2)}
What is the first derivative of 1/(sqrt(7x)) ?
The first derivative of 1/(sqrt(7x)) is -1/(2sqrt(7)x^{3/2)}