What is the derivative of f(x)= x/4 arcsin(x) ?

The derivative of f(x)= x/4 arcsin(x) is 1/4 (arcsin(x)+x/(sqrt(1-x^2)))

What is the first derivative of f(x)= x/4 arcsin(x) ?

The first derivative of f(x)= x/4 arcsin(x) is 1/4 (arcsin(x)+x/(sqrt(1-x^2)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = \frac{x}{4} arcsin (x)

\frac{1}{4} (arcsin (x) + \frac{x}{1 - x ^{2}})

Solution steps

\frac{d}{d x} (\frac{x}{4} arcsin (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{4} \frac{d}{d x} (x arcsin (x))

Apply the Product Rule:

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

f = x, g = arcsin (x)

= \frac{1}{4} (\frac{d x}{d x} arcsin (x) + \frac{d}{d x} (arcsin (x)) x)

\frac{d x}{d x} = 1

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

= \frac{1}{4} (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x)

Simplify

\frac{1}{4} (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x) : \frac{1}{4} (arcsin (x) + \frac{x}{1 - x ^{2}})

= \frac{1}{4} (arcsin (x) + \frac{x}{1 - x ^{2}})

x y^{^{'}} + y = x^{3}

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

\frac{\partial}{\partial x} (x^{3} + 8 y^{3} - 6 x y + 5)

x \to - 1 - lim (x^{3} - 3)

\frac{d}{d x} (3 a x^{2} + 2 b x + c)

What is the derivative of f(x)= x/4 arcsin(x) ?
The derivative of f(x)= x/4 arcsin(x) is 1/4 (arcsin(x)+x/(sqrt(1-x^2)))
What is the first derivative of f(x)= x/4 arcsin(x) ?
The first derivative of f(x)= x/4 arcsin(x) is 1/4 (arcsin(x)+x/(sqrt(1-x^2)))