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

The derivative of sqrt(1\sqrt{1+x)} is 1/(4(1+x)^{3/4)}

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

The first derivative of sqrt(1\sqrt{1+x)} is 1/(4(1+x)^{3/4)}

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

\frac{1}{4 ( 1 + x ) ^{\frac{3}{4}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 1 \cdot 1 + x} \cdot \frac{1}{2 1 + x} : \frac{1}{4 ( 1 + x ) ^{\frac{3}{4}}}

= \frac{1}{4 ( 1 + x ) ^{\frac{3}{4}}}

What is the derivative of sqrt(1\sqrt{1+x)} ?
The derivative of sqrt(1\sqrt{1+x)} is 1/(4(1+x)^{3/4)}
What is the first derivative of sqrt(1\sqrt{1+x)} ?
The first derivative of sqrt(1\sqrt{1+x)} is 1/(4(1+x)^{3/4)}