What is (\partial)/(\partial x)(sqrt(\sqrt{x+1)+1}) ?

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

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(\partial)/(\partial x)(sqrt(\sqrt{x+1)+1})

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (x^{2} y^{2} z)

(2 x^{2} - 1)^{- 1}

\int_{- 2}^{2} 1 + 100 x^{2} d x

f (x) = - cot (x)

\int (3 x^{3} + 6 x^{2} - 12 x + 5) d x

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