# 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 explanation

Problem to solve:

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

Learn how to solve integrals of rational functions problems step by step online.

$y=x^{\frac{3}{x}}$

Learn how to solve integrals of rational functions problems step by step online. Find the derivative using logarithmic differentiation method (d/dx)(x^(3/x)). To derive the function {x}^{\frac{3}{x}}, use the method logarithmic differentiation. First, assign the function to y, then take the natural logarithm of both sides of the equation. Apply logarithm to both sides of the equality. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Derive both sides of the equality with respect to x.

$y^{\prime}=\frac{3x^{\frac{3}{x}}-3x^{\frac{3}{x}}\ln\left(x\right)}{x^2}$

### Problem Analysis

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

### Main topic:

Integrals of Rational Functions

~ 2.86 seconds