What is the derivative of arcsin(x^2+1) ?

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

What is the first derivative of arcsin(x^2+1) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (arcsin (x^{2} + 1))

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

Solution steps

\frac{d}{d x} (arcsin (x^{2} + 1))

Apply the chain rule:

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

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

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

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

Simplify

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

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

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