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# Find the derivative $\frac{d}{dx}\left(8\sqrt{x}+\frac{7}{x^5}\right)$ using the sum rule

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##  Final answer to the problem

$\frac{4\sqrt{x^{11}}-35}{x^{6}}$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Find the derivative using the definition
• Find the derivative using the product rule
• Find the derivative using the quotient rule
• Find the derivative using logarithmic differentiation
• Find the derivative
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
• Integrate by substitution
Can't find a method? Tell us so we can add it.
1

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

$\frac{d}{dx}\left(8\sqrt{x}\right)+\frac{d}{dx}\left(\frac{7}{x^5}\right)$

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

$\frac{d}{dx}\left(8\sqrt{x}\right)+\frac{d}{dx}\left(\frac{7}{x^5}\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(8x^(1/2)+7/(x^5)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the 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}. Multiply the fraction and term in 8\cdot \left(\frac{1}{2}\right)x^{-\frac{1}{2}}.

##  Final answer to the problem

$\frac{4\sqrt{x^{11}}-35}{x^{6}}$

##  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

SnapXam A2

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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: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.