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

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

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Answer 1 · 2016-02-09T04:36:34

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

Explanation:

First, I assume you know that the derivative of $cot x$ $cotx$ is $- {csc}^{2} x$ $-csc^2x$ .

We substitute $u = 3 x$ $u=3x$ .

Therefore,

$\frac{d u}{d x} = 3$ $frac{du}{dx} = 3$ .

Now we use the chain rule.

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

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

$= - {csc}^{2} (u) \cdot 3$ $= -csc^2(u) * 3$

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

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

1 Answer

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