What is the derivative of 2sqrt(x-2) ?

The derivative of 2sqrt(x-2) is 1/(sqrt(x-2))

What is the first derivative of 2sqrt(x-2) ?

The first derivative of 2sqrt(x-2) is 1/(sqrt(x-2))

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\frac{d}{d x} (2 x - 2)

\frac{1}{x - 2}

Solution steps

\frac{d}{d x} (2 x - 2)

Take the constant out:

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

= 2 \frac{d}{d x} (x - 2)

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x - 2}

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What is the derivative of 2sqrt(x-2) ?
The derivative of 2sqrt(x-2) is 1/(sqrt(x-2))
What is the first derivative of 2sqrt(x-2) ?
The first derivative of 2sqrt(x-2) is 1/(sqrt(x-2))