en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of arcsin(1-x^2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of ((x^3-1))/(x^2(x-2)^3)

\int \frac{( x ^{3} - 1 )}{x ^{2} ( x - 2 ) ^{3}} d x

(\partial)/(\partial x)(e^{1+y-x})

\frac{\partial}{\partial x} (e^{1 + y - x})

integral of sqrt(3x)-2/(sqrt(x))

\int 3 x - \frac{2}{x} d x

y^'=y-t,y(0)=0.5

y^{^{'}} = y - t, y (0) = 0.5

integral of (4/(x^3))

\int (\frac{4}{x ^{3}}) d x

Frequently Asked Questions (FAQ)

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