What is (\partial)/(\partial x)(sqrt(x+\sqrt{x)}) ?

The answer to (\partial)/(\partial x)(sqrt(x+\sqrt{x)}) is (2sqrt(x)+1)/(4sqrt(x)\sqrt{x+\sqrt{x)}}

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(\partial)/(\partial x)(sqrt(x+\sqrt{x)})

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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}

\int \frac{1}{( x - 4 ) ^{2}} d x

\frac{d}{d x} (sin (2 x) + cos^{2} (x))

\frac{d}{d x} (4 ln (5 x))

\frac{d}{d x} ((x - 4) e^{3 x})

e^{- 2 x}

What is (\partial)/(\partial x)(sqrt(x+\sqrt{x)}) ?
The answer to (\partial)/(\partial x)(sqrt(x+\sqrt{x)}) is (2sqrt(x)+1)/(4sqrt(x)\sqrt{x+\sqrt{x)}}