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Factor the expression $x^2-2x+1$

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Final answer to the problem

$2x-2$
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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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1

Find the derivative of $x^2-2x+1$ 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 $x^2-2x+1$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get

$\lim_{h\to0}\left(\frac{\left(x+h\right)^2-2\left(x+h\right)+1-\left(x^2-2x+1\right)}{h}\right)$

Learn how to solve definition of derivative problems step by step online.

$\lim_{h\to0}\left(\frac{\left(x+h\right)^2-2\left(x+h\right)+1-\left(x^2-2x+1\right)}{h}\right)$

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Learn how to solve definition of derivative problems step by step online. Factor the expression x^2-2x+1. Find the derivative of x^2-2x+1 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 x^2-2x+1. Substituting f(x+h) and f(x) on the limit, we get. Expand the expression \left(x+h\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Multiply the single term -2 by each term of the polynomial \left(x+h\right). Solve the product -\left(x^2-2x+1\right).

Final answer to the problem

$2x-2$

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Function Plot

Plotting: $2x-2$

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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.

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