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

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

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

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

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derivative of

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

\frac{1}{x ^{\frac{1}{2}}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Power Rule:

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

= 2 \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

2 \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{1}{x ^{\frac{1}{2}}}

= \frac{1}{x ^{\frac{1}{2}}}

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