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

Simplify

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

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

(0, - 4), (1, 2)

x y^{^{'}} + 3 y = 3 e^{x}

(1 - 5 y + x) \frac{d y}{d x} + y = 5 x - 1

y^{'} (t) = 10 - e^{y}, y (0) = 1

y = x^{3} - \frac{x ^{2}}{16}

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)}}