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Find the derivative $\frac{d}{dx}\left(9x^4\ln\left(x^4\right)+\ln\left(x\right)^5\right)$ using the sum rule

Step-by-step Solution

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Final answer to the problem

$\frac{36x^{4}\ln\left(x^4\right)+36x^{4}+5\ln\left(x\right)^{4}}{x}$
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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

$\frac{d}{dx}\left(9x^4\ln\left(x^4\right)\right)+\frac{d}{dx}\left(\ln\left(x\right)^5\right)$

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

$\frac{d}{dx}\left(9x^4\ln\left(x^4\right)\right)+\frac{d}{dx}\left(\ln\left(x\right)^5\right)$

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(9x^4ln(x^4)+ln(x)^5) 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. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

Final answer to the problem

$\frac{36x^{4}\ln\left(x^4\right)+36x^{4}+5\ln\left(x\right)^{4}}{x}$

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Function Plot

Plotting: $\frac{36x^{4}\ln\left(x^4\right)+36x^{4}+5\ln\left(x\right)^{4}}{x}$

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7
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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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