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Find the derivative of $x\left(x^2+1\right)$

Step-by-step Solution

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 Solution

$x^2+1+2x^2$
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 Step-by-step Solution 

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1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=x^2+1$

$\frac{d}{dx}\left(x\right)\left(x^2+1\right)+x\frac{d}{dx}\left(x^2+1\right)$

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$\frac{d}{dx}\left(x\right)\left(x^2+1\right)+x\frac{d}{dx}\left(x^2+1\right)$

Learn how to solve problems step by step online. Find the derivative of x(x^2+1). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=x^2+1. The derivative of the linear function is equal to 1. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (1) is equal to zero.

$x^2+1+2x^2$

 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

Find the derivativeFind derivative of x(x^2+1) using the product ruleFind derivative of x(x^2+1) using the quotient ruleFind derivative of x(x^2+1) using logarithmic differentiationFind derivative of x(x^2+1) using the definition

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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