How do you differentiate #f(x)=cot(3x) # using the chain rule?

1 Answer
Bio
Feb 9, 2016

#frac{du}{dx} = -3csc^2(3x)#

Explanation:

First, I assume you know that the derivative of #cotx# is #-csc^2x#.

We substitute #u=3x#.

Therefore,

#frac{du}{dx} = 3#.

Now we use the chain rule.

#frac{d}{dx}(cot(3x)) = frac{d}{dx}(cot(u))#

#= frac{d}{du}(cot(u))*frac{du}{dx}#

# = -csc^2(u) * 3#

#= -3csc^2(3x)#

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