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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = cos^{6} (x)

x \to 4 lim (x (x + 5) (x + 6))

\frac{d ^{4}}{d x ^{4}} (3 ln (x))

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{6})

x \to 5 lim (3)

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