Find the derivative of $2x-3\left(x-3\right)^2$ using the definition

Step-by-step Solution

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Final answer to the problem

$20-6x$
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Step-by-step Solution

How should I solve this problem?

  • Find the derivative using the definition
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Prove from LHS (left-hand side)
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A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: $(a-b)^2=a^2-2ab+b^2$

$derivdef\left(2x-3\left(x^2-6x+9\right)\right)$

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$derivdef\left(2x-3\left(x^2-6x+9\right)\right)$

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Learn how to solve definition of derivative problems step by step online. Find the derivative of 2x-3(x-3)^2 using the definition. A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: (a-b)^2=a^2-2ab+b^2. Multiply the single term -3 by each term of the polynomial \left(x^2-6x+9\right). Combining like terms 2x and 18x. Find the derivative of 20x-3x^2-27 using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is 20x-3x^2-27. Substituting f(x+h) and f(x) on the limit, we get.

Final answer to the problem

$20-6x$

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Plotting: $20-6x$

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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: Definition of Derivative

Resolution of derivatives using the definition of the derivative, which is the limit of difference quotients of real numbers.

Used Formulas

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