What is the derivative of sqrt(1+\sqrt{x)} ?

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

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

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

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derivative of

1 + x

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 6 x - 5 d x

\int 5 x^{4} d x

\frac{d y}{d x} + \frac{y}{x} = y^{- 2}

\frac{( t ^{3} + t )}{( t ^{4} - 2 )}

y^{^{'}} + e^{x} y = y^{2}

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