What is the derivative of x^{11}arccot(x) ?

The derivative of x^{11}arccot(x) is 11x^{10}arccot(x)-(x^{11})/(x^2+1)

What is the first derivative of x^{11}arccot(x) ?

The first derivative of x^{11}arccot(x) is 11x^{10}arccot(x)-(x^{11})/(x^2+1)

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derivative

11 x^{10} arccot (x) - \frac{x ^{11}}{x ^{2} + 1}

Solution steps

\frac{d}{d x} (x^{11} arccot (x))

Apply the Product Rule:

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

f = x^{11}, g = arccot (x)

= \frac{d}{d x} (x^{11}) arccot (x) + \frac{d}{d x} (arccot (x)) x^{11}

\frac{d}{d x} (x^{11}) = 11 x^{10}

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

= 11 x^{10} arccot (x) + (- \frac{1}{x ^{2} + 1}) x^{11}

Simplify

11 x^{10} arccot (x) + (- \frac{1}{x ^{2} + 1}) x^{11} : 11 x^{10} arccot (x) - \frac{x ^{11}}{x ^{2} + 1}

= 11 x^{10} arccot (x) - \frac{x ^{11}}{x ^{2} + 1}

What is the derivative of x^{11}arccot(x) ?
The derivative of x^{11}arccot(x) is 11x^{10}arccot(x)-(x^{11})/(x^2+1)
What is the first derivative of x^{11}arccot(x) ?
The first derivative of x^{11}arccot(x) is 11x^{10}arccot(x)-(x^{11})/(x^2+1)