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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

1 - x^{2} arcsin (x)

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 1 - x^{2}, g = arcsin (x)

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

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

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

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

Simplify

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

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

\frac{d}{d y} (arctan (\frac{x - y}{x}))

\frac{\partial}{\partial x} (\frac{( x - y )}{c ( a - b )})

\frac{d}{d t} (8 t)

\int \frac{5}{3} d x

\int_{6}^{8} \frac{x}{x ^{2} + 6 x + 13} d x

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