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Find the derivative $\frac{d}{dx}\left(2x\sin\left(x\right)+3x\cos\left(x\right)\right)$ using the sum rule

Step-by-step Solution

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$2\left(\sin\left(x\right)+x\cos\left(x\right)\right)+3\left(\cos\left(x\right)-x\sin\left(x\right)\right)$
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Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(2x\cdot\sin\left(x\right)+3x\cdot\cos\left(x\right)\right)$

Specify the solving method

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

$\frac{d}{dx}\left(2x\sin\left(x\right)\right)+\frac{d}{dx}\left(3x\cos\left(x\right)\right)$

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

$\frac{d}{dx}\left(2x\sin\left(x\right)\right)+\frac{d}{dx}\left(3x\cos\left(x\right)\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative (d/dx)(2xsin(x)+3xcos(x)) 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. The derivative of a function multiplied by a constant (3) 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 and g=\sin\left(x\right).

$2\left(\sin\left(x\right)+x\cos\left(x\right)\right)+3\left(\cos\left(x\right)-x\sin\left(x\right)\right)$

Explore different ways to solve this problem

Find the derivativeProduct ruleQuotient ruleLogarithmic differentiation
SnapXam A2

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1
2
3
4
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

Useful tips on how to improve your answer:

$\frac{d}{dx}\left(2x\cdot\sin\left(x\right)+3x\cdot\cos\left(x\right)\right)$

Main topic:

Sum Rule of Differentiation

~ 0.11 s