What is the derivative of (1+x^{-1/2}) ?

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

What is the first derivative of (1+x^{-1/2}) ?

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

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

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

Solution steps

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

Apply the chain rule:

- \frac{1}{2 ( 1 + x ) ^{\frac{3}{2}}} \frac{d}{d x} (1 + x)

= - \frac{1}{2 ( 1 + x ) ^{\frac{3}{2}}} \frac{d}{d x} (1 + x)

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

= - \frac{1}{2 ( 1 + x ) ^{\frac{3}{2}}} \cdot 1

Simplify

= - \frac{1}{2 ( 1 + x ) ^{\frac{3}{2}}}

y^{^{'}} = - sin (x) - sin (x) y, y (0) = 8

x \to 0 + lim (\frac{1}{e ^{x} - 1})

y^{^{''}} + 16 y = sec^{2} (4 x)

\frac{x ^{3}}{6}

3 x y - 2 π cos (y) = 20 π, (6, π)

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