What is the derivative of x^2arctan(8x) ?

The derivative of x^2arctan(8x) is 2xarctan(8x)+(8x^2)/(64x^2+1)

What is the first derivative of x^2arctan(8x) ?

The first derivative of x^2arctan(8x) is 2xarctan(8x)+(8x^2)/(64x^2+1)

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\frac{d}{d x} (x^{2} arctan (8 x))

2 x arctan (8 x) + \frac{8 x ^{2}}{64 x ^{2} + 1}

Solution steps

\frac{d}{d x} (x^{2} arctan (8 x))

Apply the Product Rule:

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

f = x^{2}, g = arctan (8 x)

= \frac{d}{d x} (x^{2}) arctan (8 x) + \frac{d}{d x} (arctan (8 x)) x^{2}

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

\frac{d}{d x} (arctan (8 x)) = \frac{8}{64 x ^{2} + 1}

= 2 x arctan (8 x) + \frac{8}{64 x ^{2} + 1} x^{2}

Multiply fractions:

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

= 2 x arctan (8 x) + \frac{8 x ^{2}}{64 x ^{2} + 1}

\int 9 cos (t) d t

\frac{ln ( x )}{x}

\int \frac{x ^{2} - 3 x - 10}{x + 2} d x

x \to 0 + lim (x cos (\frac{3}{x}))

x \to 1 + lim (2 x - 1)

What is the derivative of x^2arctan(8x) ?
The derivative of x^2arctan(8x) is 2xarctan(8x)+(8x^2)/(64x^2+1)
What is the first derivative of x^2arctan(8x) ?
The first derivative of x^2arctan(8x) is 2xarctan(8x)+(8x^2)/(64x^2+1)