What is the derivative of f(x)=(sqrt(x))/2 ?

The derivative of f(x)=(sqrt(x))/2 is 1/(4sqrt(x))

What is the first derivative of f(x)=(sqrt(x))/2 ?

The first derivative of f(x)=(sqrt(x))/2 is 1/(4sqrt(x))

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derivative

\frac{1}{4 x}

Solution steps

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

Take the constant out:

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

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

Apply radical rule:

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

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{2} \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{1}{4 x}

= \frac{1}{4 x}

What is the derivative of f(x)=(sqrt(x))/2 ?
The derivative of f(x)=(sqrt(x))/2 is 1/(4sqrt(x))
What is the first derivative of f(x)=(sqrt(x))/2 ?
The first derivative of f(x)=(sqrt(x))/2 is 1/(4sqrt(x))