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Find the derivative of $\ln\left(\cos\left(x\right)\right)$

Step-by-step Solution

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Solution

Formulas

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Final answer to the problem

$-\tan\left(x\right)$
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Step-by-step Solution

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Learn how to solve basic differentiation rules problems step by step online. Find the derivative of ln(cos(x)). 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). Multiply the fraction by the term . Any expression multiplied by 1 is equal to itself.

Final answer to the problem

$-\tan\left(x\right)$

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Function Plot

Plotting: $-\tan\left(x\right)$

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5
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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
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Similar Problems Solved

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

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

$\frac{d}{dx}\tan\left(x\right)$

$\frac{d}{dx}\left(\sin^2\left(x\right)\right)$

$\frac{d}{dx}\ln\left(x^2\right)$

$\frac{d}{dx}\sin\left(x^2\right)$

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

Main Topic: Basic Differentiation Rules

Some differentiation rules are very easy to remember and use. These are the basic ones: constant rule, sum rule, product rule and quotient rule.

Used Formulas

See formulas (2)

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