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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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