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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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Final Answer

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

Problem to solve:

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

Specify the solving method

1

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 sum rule of differentiation problems step by step online.

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

Unlock the first 3 steps of this solution!

Learn how to solve sum rule of differentiation 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). Solve the product -(\frac{d}{dx}\left(x\right)\cos\left(xy\right)+x\frac{d}{dx}\left(\cos\left(xy\right)\right)).

Final Answer

$2e^{2x}-\cos\left(xy\right)+xy\sin\left(xy\right)$
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Got another answer? Verify it!

Go!
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

Tips on how to improve your answer:

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

Related Formulas:

5. See formulas

Time to solve it:

~ 0.06 s