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

The derivative of sqrt(x+\sqrt{x)} is (2sqrt(x)+1)/(4sqrt(x)\sqrt{x+\sqrt{x)}}

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

The first derivative of sqrt(x+\sqrt{x)} is (2sqrt(x)+1)/(4sqrt(x)\sqrt{x+\sqrt{x)}}

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derivative of

x + x

\frac{2 x + 1}{4 x x + x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x + x} (1 + \frac{1}{2 x}) : \frac{2 x + 1}{4 x x + x}

= \frac{2 x + 1}{4 x x + x}

What is the derivative of sqrt(x+\sqrt{x)} ?
The derivative of sqrt(x+\sqrt{x)} is (2sqrt(x)+1)/(4sqrt(x)\sqrt{x+\sqrt{x)}}
What is the first derivative of sqrt(x+\sqrt{x)} ?
The first derivative of sqrt(x+\sqrt{x)} is (2sqrt(x)+1)/(4sqrt(x)\sqrt{x+\sqrt{x)}}