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

## Step-by-step Solution

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###  Videos

$\frac{-16\cdot 2^{'1}x}{\left(x^2+4\right)^2}$
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##  Step-by-step Solution 

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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 derivative of 8/(x^2+4)2^'1 using the product ruleFind derivative of 8/(x^2+4)2^'1 using the quotient ruleFind derivative of 8/(x^2+4)2^'1 using logarithmic differentiationFind derivative of 8/(x^2+4)2^'1 using the definition

SnapXam A2

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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

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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