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

The derivative of sqrt(2+\sqrt{6x)} is (sqrt(3))/(2sqrt(2)\sqrt{x)sqrt(2+\sqrt{6)sqrt(x)}}

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

The first derivative of sqrt(2+\sqrt{6x)} is (sqrt(3))/(2sqrt(2)\sqrt{x)sqrt(2+\sqrt{6)sqrt(x)}}

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

\frac{3}{2 2 x 2 + 6 x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 + 6 x) = \frac{3}{2 x}

= \frac{1}{2 2 + 6 x} \cdot \frac{3}{2 x}

Simplify

\frac{1}{2 2 + 6 x} \cdot \frac{3}{2 x} : \frac{3}{2 2 x 2 + 6 x}

= \frac{3}{2 2 x 2 + 6 x}

What is the derivative of sqrt(2+\sqrt{6x)} ?
The derivative of sqrt(2+\sqrt{6x)} is (sqrt(3))/(2sqrt(2)\sqrt{x)sqrt(2+\sqrt{6)sqrt(x)}}
What is the first derivative of sqrt(2+\sqrt{6x)} ?
The first derivative of sqrt(2+\sqrt{6x)} is (sqrt(3))/(2sqrt(2)\sqrt{x)sqrt(2+\sqrt{6)sqrt(x)}}