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# Find the derivative of $x^2$ using the definition

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##  Final Answer

$2x$
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##  Step-by-step Solution 

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

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

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

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

Learn how to solve definition of derivative problems step by step online. Find the derivative of x^2 using the definition. Find the derivative of x^2 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. Substituting f(x+h) and f(x) on the limit, we get. Expand \left(x+h\right)^2. Cancel like terms x^2 and -x^2. Factor the polynomial 2xh+h^2 by it's greatest common factor (GCF): h.

##  Final Answer

$2x$

##  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

Find the derivativeFind derivdef(x^2) using the product ruleFind derivdef(x^2) using the quotient ruleFind derivdef(x^2) using logarithmic differentiation

SnapXam A2
Answer Assistant

Go!
1
2
3
4
5
6
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

### 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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