What is the derivative of-1/(2sqrt(x)) ?

The derivative of-1/(2sqrt(x)) is 1/(4x^{3/2)}

What is the first derivative of-1/(2sqrt(x)) ?

The first derivative of-1/(2sqrt(x)) is 1/(4x^{3/2)}

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

\frac{1}{4 x ^{\frac{3}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Simplify

- \frac{1}{2} (- \frac{1}{2} x^{- \frac{1}{2} - 1}) : \frac{1}{4 x ^{\frac{3}{2}}}

= \frac{1}{4 x ^{\frac{3}{2}}}

x \to 2 lim (f (x) + 5 g (x))

\int_{0}^{9} \frac{1}{81 - t ^{2}} d t

\int sin (φ) d φ

\frac{d}{d x} (x + 1 (x - 1))

x \to 0 lim (\frac{1}{x ^{13}})

What is the derivative of-1/(2sqrt(x)) ?
The derivative of-1/(2sqrt(x)) is 1/(4x^{3/2)}
What is the first derivative of-1/(2sqrt(x)) ?
The first derivative of-1/(2sqrt(x)) is 1/(4x^{3/2)}