What is (\partial)/(\partial x)(sqrt(8-2x^2-y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(8-2x^2-y^2)) is -(2x)/(sqrt(8-2x^2-y^2))

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(\partial)/(\partial x)(sqrt(8-2x^2-y^2))

\frac{\partial}{\partial x} (8 - 2 x^{2} - y^{2})

- \frac{2 x}{8 - 2 x ^{2} - y ^{2}}

Solution steps

\frac{\partial}{\partial x} (8 - 2 x^{2} - y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 8 - 2 x ^{2} - y ^{2}} \frac{\partial}{\partial x} (8 - 2 x^{2} - y^{2})

= \frac{1}{2 8 - 2 x ^{2} - y ^{2}} \frac{\partial}{\partial x} (8 - 2 x^{2} - y^{2})

\frac{\partial}{\partial x} (8 - 2 x^{2} - y^{2}) = - 4 x

= \frac{1}{2 8 - 2 x ^{2} - y ^{2}} (- 4 x)

Simplify

\frac{1}{2 8 - 2 x ^{2} - y ^{2}} (- 4 x) : - \frac{2 x}{8 - 2 x ^{2} - y ^{2}}

= - \frac{2 x}{8 - 2 x ^{2} - y ^{2}}

g (0) = (4 - 2 x) e^{n} - 4

x \to - 1 lim (5 - x^{2})

\frac{π x}{4}

y^{^{'}} = 4 x (x - 2)

(1 + x)^{\frac{3}{2}}

What is (\partial)/(\partial x)(sqrt(8-2x^2-y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(8-2x^2-y^2)) is -(2x)/(sqrt(8-2x^2-y^2))