What is the derivative of f(s)=(sqrt(s))/4 ?

The derivative of f(s)=(sqrt(s))/4 is 1/(8sqrt(s))

What is the first derivative of f(s)=(sqrt(s))/4 ?

The first derivative of f(s)=(sqrt(s))/4 is 1/(8sqrt(s))

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derivative of

f (s) = \frac{s}{4}

\frac{1}{8 s}

Solution steps

\frac{d}{d s} (\frac{s}{4})

Take the constant out:

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

= \frac{1}{4} \frac{d}{d s} (s)

Apply radical rule:

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

= \frac{1}{4} \frac{d}{d s} (s^{\frac{1}{2}})

Apply the Power Rule:

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

= \frac{1}{4} \cdot \frac{1}{2} s^{\frac{1}{2} - 1}

Simplify

\frac{1}{4} \cdot \frac{1}{2} s^{\frac{1}{2} - 1} : \frac{1}{8 s}

= \frac{1}{8 s}

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What is the derivative of f(s)=(sqrt(s))/4 ?
The derivative of f(s)=(sqrt(s))/4 is 1/(8sqrt(s))
What is the first derivative of f(s)=(sqrt(s))/4 ?
The first derivative of f(s)=(sqrt(s))/4 is 1/(8sqrt(s))