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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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