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# Find the derivative $\frac{d}{dx}\left(e^{2x}-x\cos\left(xy\right)\right)$ using the sum rule

## Step-by-step Solution

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###  Videos

$2e^{2x}-\cos\left(xy\right)+xy\sin\left(xy\right)$
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##  Step-by-step Solution 

Problem to solve:

$\frac{d}{dx}\left(e^{2x}-x\cos\left(xy\right)\right)$

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

$\frac{d}{dx}\left(e^{2x}\right)+\frac{d}{dx}\left(-x\cos\left(xy\right)\right)$

Learn how to solve differential equations problems step by step online.

$\frac{d}{dx}\left(e^{2x}\right)+\frac{d}{dx}\left(-x\cos\left(xy\right)\right)$

Learn how to solve differential equations problems step by step online. Find the derivative d/dx(e^(2x)-xcos(xy)) 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 (-1) 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=\cos\left(xy\right). Simplify the product -(\frac{d}{dx}\left(x\right)\cos\left(xy\right)+x\frac{d}{dx}\left(\cos\left(xy\right)\right)).

$2e^{2x}-\cos\left(xy\right)+xy\sin\left(xy\right)$

##  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 (e^2x+-1x) using the product ruleFind derivative of (e^2x+-1x) using the quotient ruleFind derivative of (e^2x+-1x) using logarithmic differentiation

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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:

Differential Equations

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