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Find the derivative of $\ln\left(\frac{x}{2}\right)$

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$\frac{1}{x}$
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 Step-by-step Solution 

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1

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 $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{1}{\frac{x}{2}}\frac{d}{dx}\left(\frac{x}{2}\right)$

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

$\frac{1}{\frac{x}{2}}\frac{d}{dx}\left(\frac{x}{2}\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of ln(x/2). 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}. Divide fractions \frac{1}{\frac{x}{2}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. The derivative of a function multiplied by a constant (\frac{1}{2}) is equal to the constant times the derivative of the function. Divide 1 by 2.

$\frac{1}{x}$

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Find the derivativeFind derivative of ln(x/2) using the product ruleFind derivative of ln(x/2) using the quotient ruleFind derivative of ln(x/2) using logarithmic differentiationFind derivative of ln(x/2) using the definition

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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
|◻|
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

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.