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Step-by-step Solution

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

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Answer

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

Step-by-step explanation

Problem to solve:

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

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

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

Take out the constant from the fraction's numerator

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

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Answer

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

Main topic:

Quotient rule

Time to solve it:

~ 1.02 seconds