What is (\partial)/(\partial x)(sqrt(16-x^2)) ?

The answer to (\partial)/(\partial x)(sqrt(16-x^2)) is -x/(sqrt(16-x^2))

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(\partial)/(\partial x)(sqrt(16-x^2))

\frac{\partial}{\partial x} (16 - x^{2})

- \frac{x}{16 - x ^{2}}

Solution steps

\frac{\partial}{\partial x} (16 - x^{2})

Apply the chain rule:

\frac{1}{2 16 - x ^{2}} \frac{\partial}{\partial x} (16 - x^{2})

= \frac{1}{2 16 - x ^{2}} \frac{\partial}{\partial x} (16 - x^{2})

\frac{\partial}{\partial x} (16 - x^{2}) = - 2 x

= \frac{1}{2 16 - x ^{2}} (- 2 x)

Simplify

\frac{1}{2 16 - x ^{2}} (- 2 x) : - \frac{x}{16 - x ^{2}}

= - \frac{x}{16 - x ^{2}}

What is (\partial)/(\partial x)(sqrt(16-x^2)) ?
The answer to (\partial)/(\partial x)(sqrt(16-x^2)) is -x/(sqrt(16-x^2))