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# Find the derivative $\frac{d}{dx}\left(x^2-2x^5\ln\left(x+2\right)\right)$ using the sum rule

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##  Final answer to the problem

$2x-2\left(5x^{4}\ln\left(x+2\right)+\frac{x^5}{x+2}\right)$
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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
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1

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

$\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(-2x^5\ln\left(x+2\right)\right)$

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$\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(-2x^5\ln\left(x+2\right)\right)$

Learn how to solve problems step by step online. Find the derivative d/dx(x^2-2x^5ln(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 derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

##  Final answer to the problem

$2x-2\left(5x^{4}\ln\left(x+2\right)+\frac{x^5}{x+2}\right)$

##  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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0
a
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v
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x
y
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.
(◻)
+
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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