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# Factor the expression $2x^2+ax$

## Step-by-step Solution

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###  Videos

$x$
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##  Step-by-step Solution 

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

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

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

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

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

$x$

##  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(2x^2+ax) using the product ruleFind derivdef(2x^2+ax) using the quotient ruleFind derivdef(2x^2+ax) using logarithmic differentiation

SnapXam A2

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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.