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Find the derivative $\frac{d}{dz}\left(ye^{2xy}-z\right)$ using the sum rule

Step-by-step Solution

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Solution

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Final Answer

$-1$
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Step-by-step Solution

Problem to solve:

$\frac{d}{dz}\left(ye^{2xy}-z\right)$

Specify the solving method

1

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

$\frac{d}{dz}\left(ye^{2xy}\right)+\frac{d}{dz}\left(-z\right)$

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

$\frac{d}{dz}\left(ye^{2xy}\right)+\frac{d}{dz}\left(-z\right)$

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dz(ye^(2xy)-z) 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 the constant function (ye^{2xy}) is equal to zero. The derivative of a function multiplied by a constant (-1) is equal to the constant times the derivative of the function. The derivative of the linear function is equal to 1.

Final Answer

$-1$

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/dz(ye^(2xy)-z) using the product ruleFind d/dz(ye^(2xy)-z) using the quotient ruleFind d/dz(ye^(2xy)-z) using logarithmic differentiationFind d/dz(ye^(2xy)-z) using the definition

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1
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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
D□x
∫
∫◻
|◻|
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

How to improve your answer:

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Main topic:

Sum Rule of Differentiation

Used formulas:

4. See formulas

Time to solve it:

~ 0.04 s

Related topics:

Sum Rule of DifferentiationDifferential CalculusBasic Differentiation RulesBasic DerivativesCalculusConstant Rule for Differentiation

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