What is the derivative of sqrt(49-x^2-y^2) ?

The derivative of sqrt(49-x^2-y^2) is -(x+y\frac{dy)/(dx)}{sqrt(-x^2-y^2+49)}

What is the first derivative of sqrt(49-x^2-y^2) ?

The first derivative of sqrt(49-x^2-y^2) is -(x+y\frac{dy)/(dx)}{sqrt(-x^2-y^2+49)}

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\frac{d}{d x} (49 - x^{2} - y^{2})

- \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 49}

Solution steps

\frac{d}{d x} (49 - x^{2} - y^{2})

Apply the chain rule:

\frac{1}{2 49 - x ^{2} - y ^{2}} \frac{d}{d x} (49 - x^{2} - y^{2})

= \frac{1}{2 49 - x ^{2} - y ^{2}} \frac{d}{d x} (49 - x^{2} - y^{2})

\frac{d}{d x} (49 - x^{2} - y^{2}) = - 2 x - 2 y \frac{d y}{d x}

= \frac{1}{2 49 - x ^{2} - y ^{2}} (- 2 x - 2 y \frac{d y}{d x})

Simplify

\frac{1}{2 49 - 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} + 49}

= - \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 49}

\frac{d}{d x} (c x)

\int \frac{2}{x ^{3} + 3 x ^{2} + 2 x} d x

\int \frac{1}{a ^{2} u ^{2}} d u

f (x) = x^{2} - 4, (- 3, 5)

\frac{d y}{d t} = 1.5 y, y (0) = 100

What is the derivative of sqrt(49-x^2-y^2) ?
The derivative of sqrt(49-x^2-y^2) is -(x+y\frac{dy)/(dx)}{sqrt(-x^2-y^2+49)}
What is the first derivative of sqrt(49-x^2-y^2) ?
The first derivative of sqrt(49-x^2-y^2) is -(x+y\frac{dy)/(dx)}{sqrt(-x^2-y^2+49)}