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

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

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

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

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derivative of

g (x) = \frac{1}{x}

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

Solution steps

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

Apply exponent rule:

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

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

Simplify

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

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

\frac{6}{s} + \frac{16}{s ^{2} + 16}

\frac{d ^{2} y}{d x ^{2}} = 0

\int_{- 1}^{1} e^{x} - 1 d x

x \to - 1 + lim (x^{2} - 3)

x y d x + (1 + y) 1 - x^{2} d y = 0

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