What is the derivative of 1/(10sqrt(x)) ?

The derivative of 1/(10sqrt(x)) is -1/(20x^{3/2)}

What is the first derivative of 1/(10sqrt(x)) ?

The first derivative of 1/(10sqrt(x)) is -1/(20x^{3/2)}

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\frac{d}{d x} (\frac{1}{10 x})

- \frac{1}{20 x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{10 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{10} \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

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

= \frac{1}{10} \frac{d}{d x} (x^{- \frac{1}{2}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{10} (- \frac{1}{2} x^{- \frac{1}{2} - 1})

Simplify

\frac{1}{10} (- \frac{1}{2} x^{- \frac{1}{2} - 1}) : - \frac{1}{20 x ^{\frac{3}{2}}}

= - \frac{1}{20 x ^{\frac{3}{2}}}

14 - x^{2}, x^{2} - 4

\frac{d y}{d x} + 4 x y^{4} = 0

\frac{( x - 5 )}{x + 5}

x \to 1 lim (\frac{3 x}{x - 1} - \frac{3}{ln ( x )})

\frac{d}{d x} (\frac{sin ( 6 x )}{e ^{3 x}})

What is the derivative of 1/(10sqrt(x)) ?
The derivative of 1/(10sqrt(x)) is -1/(20x^{3/2)}
What is the first derivative of 1/(10sqrt(x)) ?
The first derivative of 1/(10sqrt(x)) is -1/(20x^{3/2)}