What is the derivative of sqrt(9x-18) ?

The derivative of sqrt(9x-18) is 3/(2sqrt(x-2))

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

The first derivative of sqrt(9x-18) is 3/(2sqrt(x-2))

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\frac{d}{d x} (9 x - 18)

\frac{3}{2 x - 2}

Solution steps

\frac{d}{d x} (9 x - 18)

Apply the chain rule:

\frac{1}{2 9 x - 18} \frac{d}{d x} (9 x - 18)

= \frac{1}{2 9 x - 18} \frac{d}{d x} (9 x - 18)

\frac{d}{d x} (9 x - 18) = 9

= \frac{1}{2 9 x - 18} \cdot 9

Simplify

\frac{1}{2 9 x - 18} \cdot 9 : \frac{3}{2 x - 2}

= \frac{3}{2 x - 2}

What is the derivative of sqrt(9x-18) ?
The derivative of sqrt(9x-18) is 3/(2sqrt(x-2))
What is the first derivative of sqrt(9x-18) ?
The first derivative of sqrt(9x-18) is 3/(2sqrt(x-2))