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

# Find the derivative using the product rule $\frac{d}{dx}\left(\frac{1}{2x+3}\right)$

## Step-by-step Solution

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

###  Solution

$\frac{-2}{\left(2x+3\right)^2}$
Got another answer? Verify it here!

##  Step-by-step Solution 

Specify the solving method

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

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

Learn how to solve problems step by step online.

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

Learn how to solve problems step by step online. Find the derivative using the product rule d/dx(1/(2x+3)). 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}}. The derivative of the constant function (1) is equal to zero. Any expression multiplied by 0 is equal to 0. x+0=x, where x is any expression.

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

##  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 1/(2x+3) using the quotient ruleFind derivative of 1/(2x+3) using logarithmic differentiationFind derivative of 1/(2x+3) using the definition

SnapXam A2

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

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account