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

Step-by-step Solution

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$\frac{-2}{x^{3}}$
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Step-by-step Solution

Problem to solve:

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

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

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

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

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

Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative (d/dx)(1/(x^2)). 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. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Simplify the fraction by x.

$\frac{-2}{x^{3}}$
SnapXam A2

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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

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