What is the derivative of x^{10}arctan(x) ?

The derivative of x^{10}arctan(x) is 10x^9arctan(x)+(x^{10})/(x^2+1)

What is the first derivative of x^{10}arctan(x) ?

The first derivative of x^{10}arctan(x) is 10x^9arctan(x)+(x^{10})/(x^2+1)

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derivative of

x^{10} arctan (x)

10 x^{9} arctan (x) + \frac{x ^{10}}{x ^{2} + 1}

Solution steps

\frac{d}{d x} (x^{10} arctan (x))

Apply the Product Rule:

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

f = x^{10}, g = arctan (x)

= \frac{d}{d x} (x^{10}) arctan (x) + \frac{d}{d x} (arctan (x)) x^{10}

\frac{d}{d x} (x^{10}) = 10 x^{9}

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

= 10 x^{9} arctan (x) + \frac{1}{x ^{2} + 1} x^{10}

\frac{1}{x ^{2} + 1} x^{10} = \frac{x ^{10}}{x ^{2} + 1}

= 10 x^{9} arctan (x) + \frac{x ^{10}}{x ^{2} + 1}

\frac{\partial}{\partial y} (15 - 5 (y + 3)^{2})

\frac{\partial}{\partial x} (7 x^{3} cos (7 x^{2} y))

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

\int_{- 2}^{3} \frac{22}{x ^{4}} d x

\frac{1}{3}

What is the derivative of x^{10}arctan(x) ?
The derivative of x^{10}arctan(x) is 10x^9arctan(x)+(x^{10})/(x^2+1)
What is the first derivative of x^{10}arctan(x) ?
The first derivative of x^{10}arctan(x) is 10x^9arctan(x)+(x^{10})/(x^2+1)