Step-by-step Solution

Find the derivative using the product rule $\frac{d}{dx}\left(x\left(x^2+1\right)\right)$

Go!
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

Final Answer

$3x^2+1$
Got a different answer? Try our new Answer Assistant!

Step-by-step Solution

Problem to solve:

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

Choose the solving method

1

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

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

Learn how to solve product rule of differentiation problems step by step online.

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

Unlock this full step-by-step solution!

Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (d/dx)(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.

Final Answer

$3x^2+1$
SnapXam A2
Answer Assistant

beta
Got another answer? Verify it!

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

Tips on how to improve your answer: