What is the derivative of this function $arc cot(x/5)$ ?

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Answer 1 · 2016-11-09T20:09:40

$d/dx arc cot(x/5 )= -5/(25+x^2)$

We can write $y=arc cot(x/5) <=>coty=x/5$

We can then differentiate implicitly:

$-csc^2y dy/dx = 1 /5$
$dy/dx= -1/(5csc^2y)$

Using the identity $1+cot^2A=csc^2A$ we have

$dy/dx = -1/(5(1+(x/5 )^2))$
$dy/dx = -1/(5(1+x^2/25 )) * 25/25$
$dy/dx = -(25)/(5(25+x^2))$
$dy/dx = -5/(25+x^2)$

What is the derivative of this function arc cot(x/5)arc cot(x/5)?