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

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Answer 1 · 2016-02-09T04:36:34

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

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.

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

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

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

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

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