What is the derivative of arcsin(ax) ?

The derivative of arcsin(ax) is a/(sqrt(1-a^2x^2))

What is the first derivative of arcsin(ax) ?

The first derivative of arcsin(ax) is a/(sqrt(1-a^2x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (arcsin (a x))

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

Solution steps

\frac{d}{d x} (arcsin (a x))

Apply the chain rule:

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

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

\frac{d}{d x} (a x) = a

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

Simplify

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

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

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