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

Answer 1

William Abdalla

# 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) #

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Answer 2

Scarlett Allison

The derivative of the function ( \text{arc cot}(\frac{x}{5}) ) is ( -\frac{1}{5(1 + (\frac{x}{5})^2)} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.