What is the derivative of-2/(5sqrt(x)) ?

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

What is the first derivative of-2/(5sqrt(x)) ?

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

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\frac{d}{d x} (- \frac{2}{5 x})

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

Solution steps

\frac{d}{d x} (- \frac{2}{5 x})

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{x ^{4}}{4} - \frac{3 x ^{2}}{4} + x - 2

\frac{d}{d x} (\frac{x + 2}{ln ( x )})

f (x) = x^{2} - 7 x + 7, (6, 1)

y^{^{''}} + 3 y^{^{'}} + 2 y = 20 e^{3 t}

\frac{3}{s ( s ^{3} + 2 s ^{2} + 2 s + 1 )}

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