What is the derivative of arcsin(sqrt(2x-1)) ?

The derivative of arcsin(sqrt(2x-1)) is 1/(sqrt(-2x+2)\sqrt{2x-1)}

What is the first derivative of arcsin(sqrt(2x-1)) ?

The first derivative of arcsin(sqrt(2x-1)) is 1/(sqrt(-2x+2)\sqrt{2x-1)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (arcsin (2 x - 1))

\frac{1}{- 2 x + 2 2 x - 1}

Solution steps

\frac{d}{d x} (arcsin (2 x - 1))

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{- 2 x + 2 2 x - 1}

f^{^{'}} (x) = 3 x

y = (x^{3} - 3 x) ln (2 x)

y^{^{'}} + y = \frac{e ^{x}}{y ^{2}}

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

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