Find the derivative of $x^x\left(3x-7\right)^4\left(9x^3+2\right)^3$

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Final answer to the problem

$\left(\ln\left(x\right)+1\right)x^x\left(3x-7\right)^4\left(9x^3+2\right)^3+x^x\left(12\left(3x-7\right)^{3}\left(9x^3+2\right)^3+81\left(3x-7\right)^4\left(9x^3+2\right)^{2}x^{2}\right)$
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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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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x^x$ and $g=\left(3x-7\right)^4\left(9x^3+2\right)^3$

$\frac{d}{dx}\left(x^x\right)\left(3x-7\right)^4\left(9x^3+2\right)^3+x^x\frac{d}{dx}\left(\left(3x-7\right)^4\left(9x^3+2\right)^3\right)$

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$\frac{d}{dx}\left(x^x\right)\left(3x-7\right)^4\left(9x^3+2\right)^3+x^x\frac{d}{dx}\left(\left(3x-7\right)^4\left(9x^3+2\right)^3\right)$

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Learn how to solve differential calculus problems step by step online. Find the derivative of x^x(3x-7)^4(9x^3+2)^3. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^x and g=\left(3x-7\right)^4\left(9x^3+2\right)^3. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(3x-7\right)^4 and g=\left(9x^3+2\right)^3. 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 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

$\left(\ln\left(x\right)+1\right)x^x\left(3x-7\right)^4\left(9x^3+2\right)^3+x^x\left(12\left(3x-7\right)^{3}\left(9x^3+2\right)^3+81\left(3x-7\right)^4\left(9x^3+2\right)^{2}x^{2}\right)$

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Function Plot

Plotting: $\left(\ln\left(x\right)+1\right)x^x\left(3x-7\right)^4\left(9x^3+2\right)^3+x^x\left(12\left(3x-7\right)^{3}\left(9x^3+2\right)^3+81\left(3x-7\right)^4\left(9x^3+2\right)^{2}x^{2}\right)$

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0
a
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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: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

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