en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of arcsin(sqrt(1-x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(dy)/(dt)=100-y,y(0)=15

\frac{d y}{d t} = 100 - y, y (0) = 15

derivative of (2x-1)^2(x^3+1)^2 derivative of

(2 x - 1)^{2} (x^{3} + 1)^{2}

derivative of y=cos((pit)/4-pi/3)derivative of

y = cos (\frac{π t}{4} - \frac{π}{3})

integral of 2/(x^5)

\int \frac{2}{x ^{5}} d x

integral of cot(u)

\int cot (u) d u

Frequently Asked Questions (FAQ)

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