What is the derivative of cos(arcsin(3x)) ?

The derivative of cos(arcsin(3x)) is -(9x)/(sqrt(1-9x^2))

What is the first derivative of cos(arcsin(3x)) ?

The first derivative of cos(arcsin(3x)) is -(9x)/(sqrt(1-9x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (cos (arcsin (3 x)))

- \frac{9 x}{1 - 9 x ^{2}}

Solution steps

\frac{d}{d x} (cos (arcsin (3 x)))

Simplify

cos (arcsin (3 x)) : 1 - 9 x^{2}

= \frac{d}{d x} (1 - 9 x^{2})

Apply the chain rule:

\frac{1}{2 1 - 9 x ^{2}} \frac{d}{d x} (1 - 9 x^{2})

= \frac{1}{2 1 - 9 x ^{2}} \frac{d}{d x} (1 - 9 x^{2})

\frac{d}{d x} (1 - 9 x^{2}) = - 18 x

= \frac{1}{2 1 - 9 x ^{2}} (- 18 x)

Simplify

\frac{1}{2 1 - 9 x ^{2}} (- 18 x) : - \frac{9 x}{1 - 9 x ^{2}}

= - \frac{9 x}{1 - 9 x ^{2}}

What is the derivative of cos(arcsin(3x)) ?
The derivative of cos(arcsin(3x)) is -(9x)/(sqrt(1-9x^2))
What is the first derivative of cos(arcsin(3x)) ?
The first derivative of cos(arcsin(3x)) is -(9x)/(sqrt(1-9x^2))