# Step-by-step Solution

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
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

## Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(\ln\left(\cos\left(3x\right)\right)\right)$

Solving method

Learn how to solve differential calculus problems step by step online.

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

Learn how to solve differential calculus problems step by step online. Find the derivative of ln(cos(3x)). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). The derivative of the linear function times a constant, is equal to the constant.

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

### Main topic:

Differential Calculus

~ 0.05 s