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Find the derivative of $\ln\left(xy\right)$

Step-by-step Solution

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Solution

Formulas

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Final answer to the problem

$\frac{1}{x}$
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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(xy). 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 a function multiplied by a constant is equal to the constant times the derivative of the function. The derivative of the linear function is equal to 1. Multiply the fraction by the term y.

Final answer to the problem

$\frac{1}{x}$

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Function Plot

Plotting: $\frac{1}{x}$

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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

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

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

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

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

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

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

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

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 (3)

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