What is the derivative of (sqrt(x)/3) ?

The derivative of (sqrt(x)/3) is 1/(6sqrt(x))

What is the first derivative of (sqrt(x)/3) ?

The first derivative of (sqrt(x)/3) is 1/(6sqrt(x))

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\frac{d}{d x} (\frac{x}{3})

\frac{1}{6 x}

Solution steps

\frac{d}{d x} (\frac{x}{3})

Take the constant out:

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

= \frac{1}{3} \frac{d}{d x} (x)

Apply radical rule:

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

= \frac{1}{3} \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}{3} \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

\frac{1}{3} \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{1}{6 x}

= \frac{1}{6 x}

What is the derivative of (sqrt(x)/3) ?
The derivative of (sqrt(x)/3) is 1/(6sqrt(x))
What is the first derivative of (sqrt(x)/3) ?
The first derivative of (sqrt(x)/3) is 1/(6sqrt(x))