What is (\partial)/(\partial x)(sqrt(50-x^2-y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(50-x^2-y^2)) is -x/(sqrt(50-x^2-y^2))

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(\partial)/(\partial x)(sqrt(50-x^2-y^2))

\frac{\partial}{\partial x} (50 - x^{2} - y^{2})

- \frac{x}{50 - x ^{2} - y ^{2}}

Solution steps

\frac{\partial}{\partial x} (50 - x^{2} - y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 50 - x ^{2} - y ^{2}} \frac{\partial}{\partial x} (50 - x^{2} - y^{2})

= \frac{1}{2 50 - x ^{2} - y ^{2}} \frac{\partial}{\partial x} (50 - x^{2} - y^{2})

\frac{\partial}{\partial x} (50 - x^{2} - y^{2}) = - 2 x

= \frac{1}{2 50 - x ^{2} - y ^{2}} (- 2 x)

Simplify

\frac{1}{2 50 - x ^{2} - y ^{2}} (- 2 x) : - \frac{x}{50 - x ^{2} - y ^{2}}

= - \frac{x}{50 - x ^{2} - y ^{2}}

\frac{d}{d x} (x e^{x} + 1)

n = 1 \sum \infty 1 - (\frac{1}{2})^{n}

x \to + (- 1) lim (arccos (x))

f (x) = \frac{9}{5 + x ^{2}}, at x = 4

f (x) = x^{2} + 3, at x = 6

What is (\partial)/(\partial x)(sqrt(50-x^2-y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(50-x^2-y^2)) is -x/(sqrt(50-x^2-y^2))