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

The derivative of x^2arctan(x^3) is 2xarctan(x^3)+(3x^4)/(x^6+1)

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

The first derivative of x^2arctan(x^3) is 2xarctan(x^3)+(3x^4)/(x^6+1)

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

2 x arctan (x^{3}) + \frac{3 x ^{4}}{x ^{6} + 1}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (arctan (x^{3})) = \frac{3 x ^{2}}{x ^{6} + 1}

= 2 x arctan (x^{3}) + \frac{3 x ^{2}}{x ^{6} + 1} x^{2}

\frac{3 x ^{2}}{x ^{6} + 1} x^{2} = \frac{3 x ^{4}}{x ^{6} + 1}

= 2 x arctan (x^{3}) + \frac{3 x ^{4}}{x ^{6} + 1}

x^{3} + 4 x^{2} + 7 x + 1

n = 2 \sum \infty \frac{6}{7 ^{n}}

x \to - 3 lim (\frac{2 x}{x ^{2} + 4})

x y^{^{'}} - 2 y = 2 x^{2}

y^{^{''}} + y^{^{'}} - 42 y = 0

What is the derivative of x^2arctan(x^3) ?
The derivative of x^2arctan(x^3) is 2xarctan(x^3)+(3x^4)/(x^6+1)
What is the first derivative of x^2arctan(x^3) ?
The first derivative of x^2arctan(x^3) is 2xarctan(x^3)+(3x^4)/(x^6+1)