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)}

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\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}

6 u + 7 u

\frac{\partial}{\partial x} ((- (3 x + 9))^{9})

sin (arcsin (x))

3 e^{t} cos (t) - 3 e^{t} sin (t)

f (x) = 5 x - 6 x^{2}

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)}