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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial y} (x y + \frac{2}{x} + \frac{4}{y})

(- 34, 74), (- 33, 44)

\frac{\partial}{\partial u} (5 u^{2} v^{3} + 2 u^{2} + 7 v)

\frac{d y}{d x} = \frac{y}{2 ( x + y )}

ln (cos^{2} (x) + sin^{2} (x))

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