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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

## Step-by-step Solution

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###  Videos

$2x-2\left(5x^{4}\ln\left(x+2\right)+\frac{x^5}{x+2}\right)$
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##  Step-by-step Solution 

Problem to solve:

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

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

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

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

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

Learn how to solve sum rule of differentiation 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 (-2) 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=x^5 and g=\ln\left(x+2\right). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

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

##  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

Find the derivativeFind derivative of (x^2+-2x^5) using the product ruleFind derivative of (x^2+-2x^5) using the quotient ruleFind derivative of (x^2+-2x^5) using logarithmic differentiation

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0
a
b
c
d
f
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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

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