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Find the derivative of $2x+1$ using the definition

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Final answer to the problem

$2$
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Step-by-step Solution

How should I solve this problem?

  • 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
  • Integrate by parts
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1

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

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

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

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Learn how to solve problems step by step online. Find the derivative of 2x+1 using the definition. Find the derivative of 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 2x+1. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 2 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(2x+1\right). Add the values 1 and -1.

Final answer to the problem

$2$

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Function Plot

Plotting: $2$

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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

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