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

The derivative of (9x)/(sqrt(x)) is 9/(2sqrt(x))

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

The first derivative of (9x)/(sqrt(x)) is 9/(2sqrt(x))

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derivative of

\frac{9 x}{x}

\frac{9}{2 x}

Solution steps

\frac{d}{d x} (\frac{9 x}{x})

Simplify

\frac{9 x}{x} : 9 x

= \frac{d}{d x} (9 x)

Take the constant out:

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

= 9 \frac{d}{d x} (x)

Apply radical rule:

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

= 9 \frac{d}{d x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= 9 \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

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

= \frac{9}{2 x}

What is the derivative of (9x)/(sqrt(x)) ?
The derivative of (9x)/(sqrt(x)) is 9/(2sqrt(x))
What is the first derivative of (9x)/(sqrt(x)) ?
The first derivative of (9x)/(sqrt(x)) is 9/(2sqrt(x))