What is the derivative of f(x)=sin(arccos(x)) ?

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

What is the first derivative of f(x)=sin(arccos(x)) ?

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

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derivative of

f (x) = sin (arccos (x))

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

Solution steps

\frac{d}{d x} (sin (arccos (x)))

Simplify

sin (arccos (x)) : 1 - x^{2}

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