What is the derivative of arccos(1-x^2) ?

The derivative of arccos(1-x^2) is (2x)/(sqrt(x^2)\sqrt{-x^2+2)}

What is the first derivative of arccos(1-x^2) ?

The first derivative of arccos(1-x^2) is (2x)/(sqrt(x^2)\sqrt{-x^2+2)}

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derivative of

arccos (1 - x^{2})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

\int \frac{1}{7 - 4 x - x ^{2}} d x

\frac{( s + 1 )}{( s ^{2} + 2 s + 9 )}

x = 3 y, x = 2 + y^{2}

6 u^{- 1}

What is the derivative of arccos(1-x^2) ?
The derivative of arccos(1-x^2) is (2x)/(sqrt(x^2)\sqrt{-x^2+2)}
What is the first derivative of arccos(1-x^2) ?
The first derivative of arccos(1-x^2) is (2x)/(sqrt(x^2)\sqrt{-x^2+2)}