Find the derivative of $x\left(2x+3\right)^2$

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Final answer to the problem

$\left(2x+3\right)\left(6x+3\right)$
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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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1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\left(2x+3\right)^2$

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

Learn how to solve differential calculus problems step by step online.

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

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Learn how to solve differential calculus problems step by step online. Find the derivative of x(2x+3)^2. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\left(2x+3\right)^2. The derivative of the linear function is equal to 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}. Any expression to the power of 1 is equal to that same expression.

Final answer to the problem

$\left(2x+3\right)\left(6x+3\right)$

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Function Plot

Plotting: $\left(2x+3\right)\left(6x+3\right)$

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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: 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

See formulas (6)

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