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

The derivative of f(x)=x^2arctan(3x) is 2xarctan(3x)+(3x^2)/(9x^2+1)

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

The first derivative of f(x)=x^2arctan(3x) is 2xarctan(3x)+(3x^2)/(9x^2+1)

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derivative of

f (x) = x^{2} arctan (3 x)

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (arctan (3 x)) = \frac{3}{9 x ^{2} + 1}

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

Multiply fractions:

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

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

What is the derivative of f(x)=x^2arctan(3x) ?
The derivative of f(x)=x^2arctan(3x) is 2xarctan(3x)+(3x^2)/(9x^2+1)
What is the first derivative of f(x)=x^2arctan(3x) ?
The first derivative of f(x)=x^2arctan(3x) is 2xarctan(3x)+(3x^2)/(9x^2+1)