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

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

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

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

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derivative of

f (x) = 1 - x^{2}

- \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}}

x^{3} sec (x) + sec (x) tan (x) x^{4}

(- 9, 4), (2, - 1)

(8, - 3), (- 5, - 9)

y = x^{2}, (3, 9)

6 x

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