What is the derivative of f(x)= 1/(sqrt(5x)) ?

The derivative of f(x)= 1/(sqrt(5x)) is -1/(2sqrt(5)x^{3/2)}

What is the first derivative of f(x)= 1/(sqrt(5x)) ?

The first derivative of f(x)= 1/(sqrt(5x)) is -1/(2sqrt(5)x^{3/2)}

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derivative of

f (x) = \frac{1}{5 x}

- \frac{1}{2 5 x ^{\frac{3}{2}}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

= - \frac{1}{2 ( 5 x ) ^{\frac{3}{2}}} \cdot 5

Simplify

- \frac{1}{2 ( 5 x ) ^{\frac{3}{2}}} \cdot 5 : - \frac{1}{2 5 x ^{\frac{3}{2}}}

= - \frac{1}{2 5 x ^{\frac{3}{2}}}

What is the derivative of f(x)= 1/(sqrt(5x)) ?
The derivative of f(x)= 1/(sqrt(5x)) is -1/(2sqrt(5)x^{3/2)}
What is the first derivative of f(x)= 1/(sqrt(5x)) ?
The first derivative of f(x)= 1/(sqrt(5x)) is -1/(2sqrt(5)x^{3/2)}