What is the derivative of sqrt(2x+6) ?

The derivative of sqrt(2x+6) is 1/(sqrt(2x+6))

What is the first derivative of sqrt(2x+6) ?

The first derivative of sqrt(2x+6) is 1/(sqrt(2x+6))

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\frac{d}{d x} (2 x + 6)

\frac{1}{2 x + 6}

Solution steps

\frac{d}{d x} (2 x + 6)

Apply the chain rule:

\frac{1}{2 2 x + 6} \frac{d}{d x} (2 x + 6)

= \frac{1}{2 2 x + 6} \frac{d}{d x} (2 x + 6)

\frac{d}{d x} (2 x + 6) = 2

= \frac{1}{2 2 x + 6} \cdot 2

Simplify

\frac{1}{2 2 x + 6} \cdot 2 : \frac{1}{2 x + 6}

= \frac{1}{2 x + 6}

What is the derivative of sqrt(2x+6) ?
The derivative of sqrt(2x+6) is 1/(sqrt(2x+6))
What is the first derivative of sqrt(2x+6) ?
The first derivative of sqrt(2x+6) is 1/(sqrt(2x+6))