What is the derivative of sqrt(4-x^2-y^2) ?

The derivative of sqrt(4-x^2-y^2) is -(x+y\frac{dy)/(dx)}{sqrt(-x^2-y^2+4)}

What is the first derivative of sqrt(4-x^2-y^2) ?

The first derivative of sqrt(4-x^2-y^2) is -(x+y\frac{dy)/(dx)}{sqrt(-x^2-y^2+4)}

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\frac{d}{d x} (4 - x^{2} - y^{2})

- \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 4}

Solution steps

\frac{d}{d x} (4 - x^{2} - y^{2})

Apply the chain rule:

\frac{1}{2 4 - x ^{2} - y ^{2}} \frac{d}{d x} (4 - x^{2} - y^{2})

= \frac{1}{2 4 - x ^{2} - y ^{2}} \frac{d}{d x} (4 - x^{2} - y^{2})

\frac{d}{d x} (4 - x^{2} - y^{2}) = - 2 x - 2 y \frac{d y}{d x}

= \frac{1}{2 4 - x ^{2} - y ^{2}} (- 2 x - 2 y \frac{d y}{d x})

Simplify

\frac{1}{2 4 - 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} + 4}

= - \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 4}

4.6553 x 1 0^{- 5} \cdot 0.0730700000000 \dots

0.7575 L^{- 0.25}

- 2 (1.67 (1 0^{- 19}))

x - 7 x x + 7

1 \cdot 1 0^{- 12} (e^{\frac{0.52}{0.026}} - 1)

What is the derivative of sqrt(4-x^2-y^2) ?
The derivative of sqrt(4-x^2-y^2) is -(x+y\frac{dy)/(dx)}{sqrt(-x^2-y^2+4)}
What is the first derivative of sqrt(4-x^2-y^2) ?
The first derivative of sqrt(4-x^2-y^2) is -(x+y\frac{dy)/(dx)}{sqrt(-x^2-y^2+4)}