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

# Quotient Rule of Differentiation Calculator

## Get detailed solutions to your math problems with our Quotient Rule of Differentiation step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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

###  Difficult Problems

1

Solved example of quotient rule of differentiation

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

Apply the quotient rule for differentiation, 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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

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

The derivative of the linear function is equal to $1$

$1\left(x^2+1\right)$

Any expression multiplied by $1$ is equal to itself

$x^2+1$
3

The derivative of the linear function is equal to $1$

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

4

The derivative of a sum of two or more functions is the sum of the derivatives of each function

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

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

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

The derivative of the constant function ($1$) is equal to zero

$\frac{x^2+1+\left(-\frac{d}{dx}\left(x^2\right)- 0\right)x}{\left(x^2+1\right)^2}$
7

Multiply $-1$ times $0$

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

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

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

Subtract the values $2$ and $-1$

$-2x$
8

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

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

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