What is the derivative of sqrt(9-x^2-y^2) ?

The derivative of sqrt(9-x^2-y^2) is -(x+y\frac{dy)/(dx)}{sqrt(-x^2-y^2+9)}

What is the first derivative of sqrt(9-x^2-y^2) ?

The first derivative of sqrt(9-x^2-y^2) is -(x+y\frac{dy)/(dx)}{sqrt(-x^2-y^2+9)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (9 - x^{2} - y^{2})

- \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 9}

Solution steps

\frac{d}{d x} (9 - x^{2} - y^{2})

Apply the chain rule:

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

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

\frac{d}{d x} (9 - x^{2} - y^{2}) = - 2 x - 2 y \frac{d y}{d x}

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

Simplify

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

= - \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 9}

What is the derivative of sqrt(9-x^2-y^2) ?
The derivative of sqrt(9-x^2-y^2) is -(x+y\frac{dy)/(dx)}{sqrt(-x^2-y^2+9)}
What is the first derivative of sqrt(9-x^2-y^2) ?
The first derivative of sqrt(9-x^2-y^2) is -(x+y\frac{dy)/(dx)}{sqrt(-x^2-y^2+9)}