What is the derivative of cot2(x) ?

Question

Foreckije · Accepted Answer

You would use the chain rule to solve this. To do that, youll

Edward Patten · Accepted Answer

f(x)=cot2x df(x)dx=2cot⁡x(−csc2⁡x) =−2csc2xcot⁡x first you get the derivative of the indice, then the trig function, lastly the x. it&#039;s easy if you remember it that way ;)

RizerMix · Accepted Answer

I like the previous answer, but I think it's simpler to use the product rule. Since
$\cot^{2} x = \cot x \cdot \cot x, \frac{d}{d x} (\cot^{2} x) = f^{'} (x) g (x) + g^{'} (x) f (x)$ where
$f (x) = g (x) = \cot x$ . This evaluate to
$\cot x \times (- \frac{1}{\sin^{2} x}) + (- \frac{1}{\sin^{2} x}) \times \cot x = 2 (- \frac{1}{\sin^{2} x}) \cot x - \frac{2 \cot x}{\sin^{2} x}$
This is equivalent to the previous answer, since $\frac{1}{\sin^{2} x} = \csc^{2} x$ , but I think that that answer is cleaner, don't you?

What is the derivative of \cot^2(x) ?

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