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

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

$2$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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0
a
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y
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◻/◻
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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