What is (\partial)/(\partial x)(sqrt(1-x^2)) ?

The answer to (\partial)/(\partial x)(sqrt(1-x^2)) is -x/(sqrt(1-x^2))

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(\partial)/(\partial x)(sqrt(1-x^2))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial y} (x^{4} sin (x y^{3}))

\int \frac{8 + x}{8 - x} d x

x \to \infty lim (\frac{lo g _{2} ( x )}{x})

f (x) = 2 x^{4}

\frac{d}{d x} (5 - 2 x^{3})

What is (\partial)/(\partial x)(sqrt(1-x^2)) ?
The answer to (\partial)/(\partial x)(sqrt(1-x^2)) is -x/(sqrt(1-x^2))