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

Step-by-step Solution

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Final Answer

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

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

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

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

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

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dy(e^(2y)-ycos(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=y and g=\cos\left(xy\right). Simplify the product -(\frac{d}{dy}\left(y\right)\cos\left(xy\right)+y\frac{d}{dy}\left(\cos\left(xy\right)\right)).

Final Answer

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

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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

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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

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Main Topic: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.

Used Formulas

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