# Step-by-step Solution

## Find the derivative of $\frac{-6}{\left(5x-1\right)^{\left(\frac{1}{3}\right)}}$

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
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

### Videos

$10\left(5x-1\right)^{-\frac{4}{3}}$

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\frac{-6}{\left(5x-1\right)^{\frac{1}{3}}}\right)$
1

Applying the quotient rule which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by $h(x) = \frac{f(x)}{g(x)}$, where ${g(x) \neq 0}$, then $h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}$

$\frac{\sqrt{5x-1}\cdot\frac{d}{dx}\left(-6\right)+6\frac{d}{dx}\left(\sqrt{5x-1}\right)}{\left(\sqrt{5x-1}\right)^2}$
2

The derivative of the constant function is equal to zero

$\frac{0\sqrt{5x-1}+6\frac{d}{dx}\left(\sqrt{5x-1}\right)}{\left(\sqrt{5x-1}\right)^2}$

$10\left(5x-1\right)^{-\frac{4}{3}}$
$\frac{d}{dx}\left(\frac{-6}{\left(5x-1\right)^{\frac{1}{3}}}\right)$

### Main topic:

Differential calculus

~ 1.6 seconds