en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of f(x)=x^2arctan(4x)

Solution

derivative of

f (x) = x^{2} arctan (4 x)

Solution

2 x arctan (4 x) + \frac{4 x ^{2}}{16 x ^{2} + 1}

Solution steps

\frac{d}{d x} (x^{2} arctan (4 x))

Apply the Product Rule:

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

f = x^{2}, g = arctan (4 x)

= \frac{d}{d x} (x^{2}) arctan (4 x) + \frac{d}{d x} (arctan (4 x)) x^{2}

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

\frac{d}{d x} (arctan (4 x)) = \frac{4}{16 x ^{2} + 1}

= 2 x arctan (4 x) + \frac{4}{16 x ^{2} + 1} x^{2}

Multiply fractions:

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

= 2 x arctan (4 x) + \frac{4 x ^{2}}{16 x ^{2} + 1}

Graph

Popular Examples

(\partial)/(\partial y)(e^x+y^2)

\frac{\partial}{\partial y} (e^{x} + y^{2})

derivative of h(x)= 7/(x^2)

d er i v a t i v e h (x) = \frac{7}{x ^{2}}

inverse oflaplace ((s+1))/((s*(s^2+s+1)))

in v erse l a pl a ce \frac{( s + 1 )}{( s \cdot ( s ^{2} + s + 1 ) )}

sum from n=5 to infinity of 1/(2^{2n)}

n = 5 \sum \infty \frac{1}{2 ^{2 n}}

tangent of f(x)=5-8x^2

t an g e n t f (x) = 5 - 8 x^{2}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^2arctan(4x) ?
The derivative of f(x)=x^2arctan(4x) is 2xarctan(4x)+(4x^2)/(16x^2+1)
What is the first derivative of f(x)=x^2arctan(4x) ?
The first derivative of f(x)=x^2arctan(4x) is 2xarctan(4x)+(4x^2)/(16x^2+1)