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Popular >

derivative of (arccot(x))^5

Solution

derivative of

(arccot (x))^{5}

Solution

- \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

Solution steps

\frac{d}{d x} ((arccot (x))^{5})

Apply the chain rule:

5 (arccot (x))^{4} \frac{d}{d x} (arccot (x))

= 5 (arccot (x))^{4} \frac{d}{d x} (arccot (x))

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

= 5 (arccot (x))^{4} (- \frac{1}{x ^{2} + 1})

Simplify

5 arccot^{4} (x) (- \frac{1}{x ^{2} + 1}) : - \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

= - \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

Popular Examples

integral of 3sin(3x)

\int 3 sin (3 x) d x

derivative of 3cos(x-5cot(x))

\frac{d}{d x} (3 cos (x) - 5 cot (x))

(xy^2)dx+(1+x^2y)dy=0

(x y^{2}) d x + (1 + x^{2} y) d y = 0

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\frac{d}{d x} (4 + \frac{8}{x})^{2} + (2 + x)^{2}

area y=sqrt(x^2-1),x=1,x=3 area

y = x^{2} - 1, x = 1, x = 3

Frequently Asked Questions (FAQ)

What is the derivative of (arccot(x))^5 ?
The derivative of (arccot(x))^5 is -(5arccot^4(x))/(x^2+1)
What is the first derivative of (arccot(x))^5 ?
The first derivative of (arccot(x))^5 is -(5arccot^4(x))/(x^2+1)