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

The derivative of x^2arctan(x^2) is 2xarctan(x^2)+(2x^3)/(x^4+1)

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

The first derivative of x^2arctan(x^2) is 2xarctan(x^2)+(2x^3)/(x^4+1)

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

2 x arctan (x^{2}) + \frac{2 x ^{3}}{x ^{4} + 1}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\frac{2 x}{x ^{4} + 1} x^{2} = \frac{2 x ^{3}}{x ^{4} + 1}

= 2 x arctan (x^{2}) + \frac{2 x ^{3}}{x ^{4} + 1}

\frac{d}{d x} (\frac{4 x}{x - 3})

x y^{2} y^{^{'}} = y^{3} - 3 x^{3}, y (1) = 3

\frac{x - 2}{x + 2}

\int x e^{9 - x^{2}} d x

(2 x^{2} + y^{2}) d x - x^{2} d y = 0

What is the derivative of x^2arctan(x^2) ?
The derivative of x^2arctan(x^2) is 2xarctan(x^2)+(2x^3)/(x^4+1)
What is the first derivative of x^2arctan(x^2) ?
The first derivative of x^2arctan(x^2) is 2xarctan(x^2)+(2x^3)/(x^4+1)