Step-by-step Solution

Find the derivative of $\frac{2\left(1-\sin\left(3x\right)\right)}{3\cos\left(3x\right)}$ using the constant rule

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$\frac{2}{3}\left(\frac{-3\cos\left(3x\right)^2+3\sin\left(3x\right)\left(1-\sin\left(3x\right)\right)}{\cos\left(3x\right)^2}\right)$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\frac{2\left(1-\sin\left(3x\right)\right)}{3\cos\left(3x\right)}\right)$
1

Take $\frac{2}{3}$ out of the fraction

$\frac{d}{dx}\left(\frac{\frac{2}{3}\left(1-\sin\left(3x\right)\right)}{\cos\left(3x\right)}\right)$
2

Take out the constant from the fraction's numerator

$\frac{d}{dx}\left(\frac{2}{3}\left(\frac{1-\sin\left(3x\right)}{\cos\left(3x\right)}\right)\right)$

$\frac{2}{3}\left(\frac{-3\cos\left(3x\right)^2+3\sin\left(3x\right)\left(1-\sin\left(3x\right)\right)}{\cos\left(3x\right)^2}\right)$
$\frac{d}{dx}\left(\frac{2\left(1-\sin\left(3x\right)\right)}{3\cos\left(3x\right)}\right)$

Constant rule

~ 0.83 seconds