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

##### 1 Answer

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

#### Explanation:

We can write

We can then differentiate implicitly:

# -csc^2y dy/dx = 1 /5#

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

Using the identity

# 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) #