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

## Step-by-step Solution

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###  Solution

$\frac{2x^{4}-2}{x^{3}}$
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##  Step-by-step Solution 

Problem to solve:

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

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

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

Learn how to solve problems step by step online.

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

Learn how to solve problems step by step online. Find the derivative d/dx(x^2+1/(x^2)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-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 \left(x^2\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2.

$\frac{2x^{4}-2}{x^{3}}$

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

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0
a
b
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g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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

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