Find the derivative using the product rule $\frac{d}{dx}\left(\sqrt{3x^2-12x+12}\right)$

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Final answer to the problem

$\frac{3x-6}{\sqrt{3x^2-12x+12}}$
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Step-by-step Solution

How should I solve this problem?

  • Find the derivative using the product rule
  • Find the derivative using the definition
  • 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
  • Integrate by parts
  • Load more...
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The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{1}{2}\left(3x^2-12x+12\right)^{-\frac{1}{2}}\frac{d}{dx}\left(3x^2-12x+12\right)$

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

$\frac{1}{2}\left(3x^2-12x+12\right)^{-\frac{1}{2}}\frac{d}{dx}\left(3x^2-12x+12\right)$

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Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx((3x^2-12x+12)^(1/2)). 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 a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=3 and g=x^2. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=-12 and g=x.

Final answer to the problem

$\frac{3x-6}{\sqrt{3x^2-12x+12}}$

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Function Plot

Plotting: $\frac{3x-6}{\sqrt{3x^2-12x+12}}$

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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: Product Rule of differentiation

The product rule is a formula used to find the derivatives of products of two or more functions. It may be stated as $(f\cdot g)'=f'\cdot g+f\cdot g'$

Used Formulas

See formulas (5)

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