What is the derivative of sqrt(9+\sqrt{9-x)} ?

The derivative of sqrt(9+\sqrt{9-x)} is -1/(4sqrt(9+\sqrt{9-x))sqrt(-x+9)}

What is the first derivative of sqrt(9+\sqrt{9-x)} ?

The first derivative of sqrt(9+\sqrt{9-x)} is -1/(4sqrt(9+\sqrt{9-x))sqrt(-x+9)}

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\frac{d}{d x} (9 + 9 - x)

- \frac{1}{4 9 + 9 - x - x + 9}

Solution steps

\frac{d}{d x} (9 + 9 - x)

Apply the chain rule:

\frac{1}{2 9 + 9 - x} \frac{d}{d x} (9 + 9 - x)

= \frac{1}{2 9 + 9 - x} \frac{d}{d x} (9 + 9 - x)

\frac{d}{d x} (9 + 9 - x) = - \frac{1}{2 - x + 9}

= \frac{1}{2 9 + 9 - x} (- \frac{1}{2 - x + 9})

Simplify

\frac{1}{2 9 + 9 - x} (- \frac{1}{2 - x + 9}) : - \frac{1}{4 9 + 9 - x - x + 9}

= - \frac{1}{4 9 + 9 - x - x + 9}

What is the derivative of sqrt(9+\sqrt{9-x)} ?
The derivative of sqrt(9+\sqrt{9-x)} is -1/(4sqrt(9+\sqrt{9-x))sqrt(-x+9)}
What is the first derivative of sqrt(9+\sqrt{9-x)} ?
The first derivative of sqrt(9+\sqrt{9-x)} is -1/(4sqrt(9+\sqrt{9-x))sqrt(-x+9)}