Find the derivative $\frac{d}{dx}\left(\frac{1}{x^7}\right)$

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Final answer to the problem

$\frac{-7}{x^{8}}$
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Step-by-step Solution

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Apply the formula: $\frac{d}{dx}\left(\frac{a}{b}\right)$$=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}$, where $a=1$ and $b=x^7$

$\frac{\frac{d}{dx}\left(1\right)x^7-\frac{d}{dx}\left(x^7\right)}{\left(x^7\right)^2}$

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$\frac{\frac{d}{dx}\left(1\right)x^7-\frac{d}{dx}\left(x^7\right)}{\left(x^7\right)^2}$

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Learn how to solve disuguaglianze problems step by step online. Find the derivative d/dx(1/(x^7)). Apply the formula: \frac{d}{dx}\left(\frac{a}{b}\right)=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}, where a=1 and b=x^7. Simplify \left(x^7\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 7 and n equals 2. Apply the formula: \frac{d}{dx}\left(c\right)=0, where c=1. Apply the formula: x+0=x, where x=-\frac{d}{dx}\left(x^7\right).

Final answer to the problem

$\frac{-7}{x^{8}}$

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Function Plot

Plotting: $\frac{-7}{x^{8}}$

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5
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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

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Main Topic: Disuguaglianze

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