# Step-by-step Solution

## Find the derivative of $\frac{1}{x^2-3x-1}$ using the constant rule

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
÷
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

### Videos

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

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\frac{1}{x^2-3x-1}\right)$
1

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

$\frac{\left(x^2-3x-1\right)\frac{d}{dx}\left(1\right)-\frac{d}{dx}\left(x^2-3x-1\right)}{\left(x^2-3x-1\right)^2}$
2

The derivative of the constant function is equal to zero

$\frac{0\left(x^2-3x-1\right)-\frac{d}{dx}\left(x^2-3x-1\right)}{\left(x^2-3x-1\right)^2}$

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

Constant rule

~ 0.61 seconds