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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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