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

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

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

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

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\frac{d}{d 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}}}

\int \frac{sin ( x ) x}{x} d x

(3 x^{2} + 3) (2 x^{2} + 1)

\int - \frac{y}{x ^{2} + y ^{2}} d x

x \to 2 lim (x^{3} - 8)

y^{^{'}} (t) = (y + 1) (y - 1), y (0) = 3

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