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# Find the derivative $\frac{d}{dx}\left(\frac{x+2}{x+1}\right)$

## Step-by-step Solution

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###  Videos

$\frac{x+1-x-2}{\left(x+1\right)^2}$
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##  Step-by-step Solution 

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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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

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

Learn how to solve quotient rule of differentiation problems step by step online.

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

Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx((x+2)/(x+1)). 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}}. Simplify the product -(x+2). The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a sum of two or more functions is the sum of the derivatives of each function.

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

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of (x+2)/(x+1) using the product ruleFind derivative of (x+2)/(x+1) using the quotient ruleFind derivative of (x+2)/(x+1) using logarithmic differentiationFind derivative of (x+2)/(x+1) using the definition

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0
a
b
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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

### Main Topic: Quotient Rule of Differentiation

The quotient rule is a formal rule for differentiating problems where one function is divided by another.