👉 Try now NerdPal! Our new math app on iOS and Android

# Find the derivative of $2^{'1}\frac{8}{x^2+4}$

## 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

###  Videos

$\frac{-16\cdot 2^{'1}x}{\left(x^2+4\right)^2}$
Got another answer? Verify it here!

##  Step-by-step Solution 

Problem to solve:

$\frac{d}{dx}\left(2^{'1}\frac{8}{x^2+4}\right)$

Specify the solving method

1

Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(\frac{8\cdot 2^{'1}}{x^2+4}\right)$

Learn how to solve differential calculus problems step by step online.

$\frac{d}{dx}\left(\frac{8\cdot 2^{'1}}{x^2+4}\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of 8/(x^2+4)2^'1. Simplify the derivative by applying the properties of logarithms. 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 (8\cdot 2^{'1}) is equal to zero. Any expression multiplied by 0 is equal to 0.

$\frac{-16\cdot 2^{'1}x}{\left(x^2+4\right)^2}$

##  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 d/dx(8/(x^2+4)2^'1) using the product ruleFind d/dx(8/(x^2+4)2^'1) using the quotient ruleFind d/dx(8/(x^2+4)2^'1) using logarithmic differentiationFind d/dx(8/(x^2+4)2^'1) 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

### Main topic:

Differential Calculus

~ 0.1 s

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

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