en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sin(2arccos(x))

Solution

derivative of

sin (2 arccos (x))

Solution

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

Solution steps

\frac{d}{d x} (sin (2 arccos (x)))

Apply the chain rule:

cos (2 arccos (x)) \frac{d}{d x} (2 arccos (x))

= cos (2 arccos (x)) \frac{d}{d x} (2 arccos (x))

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

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

Simplify

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

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

Popular Examples

integral from 0 to pi/(18) of cos(6x)

\int_{0}^{\frac{π}{18}} cos (6 x) d x

integral from 0 to x of 0

\int_{0}^{x} 0

limit as x approaches+0+of ln(9/(x^3))

x \to + 0 + lim (ln (\frac{9}{x ^{3}}))

integral of 25cos^2(x)

\int 25 cos^{2} (x) d x

(\partial)/(\partial x)(ln(2x))

\frac{\partial}{\partial x} (ln (2 x))

Frequently Asked Questions (FAQ)

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