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# Derive the function (2(1-1sin(3x)))/(3cos(3x)) with respect to x

### Videos

$\frac{18\left(1-\sin\left(3x\right)\right)\sin\left(3x\right)-18\cos\left(3x\right)^2}{9\cos\left(3x\right)^2}$

## Step-by-step explanation

Problem

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

Applying the quotient rule which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

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

$\frac{18\left(1-\sin\left(3x\right)\right)\sin\left(3x\right)-18\cos\left(3x\right)^2}{9\cos\left(3x\right)^2}$
$\frac{d}{dx}\left(\frac{2\left(1-\sin\left(3x\right)\right)}{3\cos\left(3x\right)}\right)$