Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

Find the derivative using the quotient rule $\frac{d}{dx}\left(\frac{x^2}{x^2-4}\right)$

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

Answer

$\frac{2x\left(x^2-4\right)-2x^{3}}{\left(x^2-4\right)^2}$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\frac{x^2}{x^2-4}\right)$
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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

$\frac{\left(x^2-4\right)\frac{d}{dx}\left(x^2\right)-x^2\frac{d}{dx}\left(x^2-4\right)}{\left(x^2-4\right)^2}$
2

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{2x\left(x^2-4\right)-x^2\frac{d}{dx}\left(x^2-4\right)}{\left(x^2-4\right)^2}$

Unlock this step-by-step solution!

Answer

$\frac{2x\left(x^2-4\right)-2x^{3}}{\left(x^2-4\right)^2}$
$\frac{d}{dx}\left(\frac{x^2}{x^2-4}\right)$

Main topic:

Quotient rule

Time to solve it:

~ 1.53 seconds