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

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

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

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

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derivative of

f (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 ((x + 1) (3 x^{2} - 9))

2 x^{2} + 5, [- 2, 3]

x \to 1 lim (\frac{∣ 1 - x ∣}{1 - x})

y^{^{''}} + y = 7 sin (x)

\frac{d}{d x} (ln (x^{8} y))

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