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Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(\frac{5x-x^2}{xe^x-3\log \left(x\right)}\right)$

Used Formulas

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Solution

Formulas

Videos

Basic Derivatives

· Derivative of the natural logarithm
$\frac{d}{dx}\left(\ln\left(x\right)\right)=\frac{1}{x}\frac{d}{dx}\left(x\right)$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$
· Sum Rule for Differentiation
$\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}f\left(x\right) + \frac{d}{dx}g\left(x\right)$
$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
$\frac{d}{dx}\left(\frac{x}{c}\right)=\frac{1}{c}\frac{d}{dx}\left(x\right)$
· Product rule for derivatives
$\frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right)$
· Power rule for derivatives
$\frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}$

Function Plot

Plotting: $\left(\frac{5-2x}{5x-x^2}+\frac{-\ln\left(10\right)}{\ln\left(10\right)xe^x-3\ln\left(x\right)}\left(e^x+xe^x+\frac{-3}{\ln\left(10\right)x}\right)\right)\frac{5x-x^2}{xe^x-3\log \left(x\right)}$

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7
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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

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Similar Problems Solved

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Find the derivative

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Find the derivative

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Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(x^{2x+3}\right)$

Main Topic: Logarithmic Differentiation

The logarithmic derivative of a function f(x) is defined by the formula f'(x)/f(x).

Used Formulas

See formulas (7)

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