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

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

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

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

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derivative of

arccos (1 - x^{2})

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

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

Simplify

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

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

y = 2 x^{2} + 5 x

\int (x + \frac{1}{9 x}) d x

\int ln (1 + x^{3}) d x

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 4, y^{^{'}} (0) = 7

\frac{\partial}{\partial z} (x^{2} + y^{2} + z^{2})

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