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

Step-by-step Solution

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Final answer to the problem

$2e^xy+\frac{1}{y}$
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Step-by-step Solution

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  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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The derivative of a sum of two or more functions is the sum of the derivatives of each function

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

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

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dy(y^2e^x+ln(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 is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}.

Final answer to the problem

$2e^xy+\frac{1}{y}$

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Function Plot

Plotting: $2e^xy+\frac{1}{y}$

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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

How to improve your answer:

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

See formulas (5)

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