What is (\partial)/(\partial x)(sqrt(25-x^2)) ?

The answer to (\partial)/(\partial x)(sqrt(25-x^2)) is -x/(sqrt(25-x^2))

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(\partial)/(\partial x)(sqrt(25-x^2))

\frac{\partial}{\partial x} (25 - x^{2})

- \frac{x}{25 - x ^{2}}

Solution steps

\frac{\partial}{\partial x} (25 - x^{2})

Apply the chain rule:

\frac{1}{2 25 - x ^{2}} \frac{\partial}{\partial x} (25 - x^{2})

= \frac{1}{2 25 - x ^{2}} \frac{\partial}{\partial x} (25 - x^{2})

\frac{\partial}{\partial x} (25 - x^{2}) = - 2 x

= \frac{1}{2 25 - x ^{2}} (- 2 x)

Simplify

\frac{1}{2 25 - x ^{2}} (- 2 x) : - \frac{x}{25 - x ^{2}}

= - \frac{x}{25 - x ^{2}}

\frac{d y}{d x} + \frac{1}{x + 8} y = x^{- 2}

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

f (x) = x^{4} + 9 e^{x}, (0, 9)

e^{x} y d y = (e^{- y} + e^{- 2 x - y}) d x

n = 0 \sum \infty \frac{n + 1}{n !}

What is (\partial)/(\partial x)(sqrt(25-x^2)) ?
The answer to (\partial)/(\partial x)(sqrt(25-x^2)) is -x/(sqrt(25-x^2))