# 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

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
÷
2

e
π
ln
log
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Videos

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

## 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