What is the derivative of 18sqrt(x) ?

The derivative of 18sqrt(x) is 9/(sqrt(x))

What is the first derivative of 18sqrt(x) ?

The first derivative of 18sqrt(x) is 9/(sqrt(x))

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derivative of

18 x

\frac{9}{x}

Solution steps

\frac{d}{d x} (18 x)

Take the constant out:

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

= 18 \frac{d}{d x} (x)

Apply radical rule:

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

= 18 \frac{d}{d x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= 18 \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

18 \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{9}{x}

= \frac{9}{x}

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What is the derivative of 18sqrt(x) ?
The derivative of 18sqrt(x) is 9/(sqrt(x))
What is the first derivative of 18sqrt(x) ?
The first derivative of 18sqrt(x) is 9/(sqrt(x))