ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Find the derivative $\frac{d}{dx}\left(\frac{x^2\sqrt{3x-2}}{\left(x-1\right)^2}\right)$

## Step-by-step Solution

Go!
Math mode
Text mode
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
|◻|
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

###  Solution

$\left(\frac{2}{x}+\frac{3}{2\left(3x-2\right)}+\frac{-2}{x-1}\right)\frac{x^2\sqrt{3x-2}}{\left(x-1\right)^2}$
Got another answer? Verify it here!

##  Step-by-step Solution 

Specify the solving method

1

To derive the function $\frac{x^2\sqrt{3x-2}}{\left(x-1\right)^2}$, use the method of logarithmic differentiation. First, assign the function to $y$, then take the natural logarithm of both sides of the equation

$y=\frac{x^2\sqrt{3x-2}}{\left(x-1\right)^2}$

Learn how to solve problems step by step online.

$y=\frac{x^2\sqrt{3x-2}}{\left(x-1\right)^2}$

Learn how to solve problems step by step online. Find the derivative d/dx((x^2(3x-2)^1/2)/((x-1)^2)). To derive the function \frac{x^2\sqrt{3x-2}}{\left(x-1\right)^2}, use the method of logarithmic differentiation. First, assign the function to y, then take the natural logarithm of both sides of the equation. Apply natural logarithm to both sides of the equality. Apply logarithm properties to both sides of the equality. Derive both sides of the equality with respect to x.

$\left(\frac{2}{x}+\frac{3}{2\left(3x-2\right)}+\frac{-2}{x-1}\right)\frac{x^2\sqrt{3x-2}}{\left(x-1\right)^2}$

SnapXam A2

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
|◻|
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