What is the derivative of y=sqrt(1-x^2) ?

The derivative of y=sqrt(1-x^2) is -x/(sqrt(1-x^2))

What is the first derivative of y=sqrt(1-x^2) ?

The first derivative of y=sqrt(1-x^2) is -x/(sqrt(1-x^2))

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derivative

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d 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}}

What is the derivative of y=sqrt(1-x^2) ?
The derivative of y=sqrt(1-x^2) is -x/(sqrt(1-x^2))
What is the first derivative of y=sqrt(1-x^2) ?
The first derivative of y=sqrt(1-x^2) is -x/(sqrt(1-x^2))