What is the derivative of f(x)=x^2arcsin(3x) ?

The derivative of f(x)=x^2arcsin(3x) is 2xarcsin(3x)+(3x^2)/(sqrt(1-9x^2))

What is the first derivative of f(x)=x^2arcsin(3x) ?

The first derivative of f(x)=x^2arcsin(3x) is 2xarcsin(3x)+(3x^2)/(sqrt(1-9x^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) = x^{2} arcsin (3 x)

2 x arcsin (3 x) + \frac{3 x ^{2}}{1 - 9 x ^{2}}

Solution steps

\frac{d}{d x} (x^{2} arcsin (3 x))

Apply the Product Rule:

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

f = x^{2}, g = arcsin (3 x)

= \frac{d}{d x} (x^{2}) arcsin (3 x) + \frac{d}{d x} (arcsin (3 x)) x^{2}

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

\frac{d}{d x} (arcsin (3 x)) = \frac{3}{1 - 9 x ^{2}}

= 2 x arcsin (3 x) + \frac{3}{1 - 9 x ^{2}} x^{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 2 x arcsin (3 x) + \frac{3 x ^{2}}{1 - 9 x ^{2}}

f (x) = x^{5} e^{x}

\frac{d r}{d θ} = (sin (π θ))^{4}

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

f (x) = 3 e^{x}

\int x cos (2 π x^{2}) d x

What is the derivative of f(x)=x^2arcsin(3x) ?
The derivative of f(x)=x^2arcsin(3x) is 2xarcsin(3x)+(3x^2)/(sqrt(1-9x^2))
What is the first derivative of f(x)=x^2arcsin(3x) ?
The first derivative of f(x)=x^2arcsin(3x) is 2xarcsin(3x)+(3x^2)/(sqrt(1-9x^2))