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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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