What is (\partial)/(\partial x)(sqrt(4-x^2-2y)) ?

The answer to (\partial)/(\partial x)(sqrt(4-x^2-2y)) is -x/(sqrt(4-x^2-2y))

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(\partial)/(\partial x)(sqrt(4-x^2-2y))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

9 x, \frac{3}{4} x, 70 - x^{2}

g (x) = 3 x^{2} lo g_{3} (x)

\frac{d}{d x} (\frac{x ^{3}}{e ^{2 x}})

\int \frac{4}{15} t^{\frac{5}{2}} + 2 cos (t) + Ct + C d t

What is (\partial)/(\partial x)(sqrt(4-x^2-2y)) ?
The answer to (\partial)/(\partial x)(sqrt(4-x^2-2y)) is -x/(sqrt(4-x^2-2y))