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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{2}{4 x - 17}

\frac{d}{d x} (cos (x) - 2 x y)

y^{^{'}} + 4 y = cos (4 t), y (0) = 2

\frac{1}{3} x^{\frac{3}{2}} - x^{\frac{1}{2}}

\int \frac{1}{x ^{3}} d x

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