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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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