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# Find the derivative $\frac{d}{dx}\left(\sin\left(x\right)+x\cos\left(x\right)\right)$ using the sum rule

## Step-by-step Solution

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$2\cos\left(x\right)-x\sin\left(x\right)$
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##  Step-by-step Solution 

Problem to solve:

$\frac{d}{dx}\left(\sin\left(x\right)+x\cos\left(x\right)\right)$

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

$\frac{d}{dx}\left(\sin\left(x\right)\right)+\frac{d}{dx}\left(x\cos\left(x\right)\right)$

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

$\frac{d}{dx}\left(\sin\left(x\right)\right)+\frac{d}{dx}\left(x\cos\left(x\right)\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(sin(x)+cos(x)x) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\cos\left(x\right) and g=x. The derivative of the linear function is equal to 1. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}.

$2\cos\left(x\right)-x\sin\left(x\right)$

##  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 d/dx(sin(x)+cos(x)x) using the product ruleFind d/dx(sin(x)+cos(x)x) using the quotient ruleFind d/dx(sin(x)+cos(x)x) using logarithmic differentiation

SnapXam A2

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0
a
b
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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

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