Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

Find the higher order derivative of $x\cos\left(x\right)$

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
÷
2

e
π
ln
log
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Answer

$-\sin\left(x\right)-\left(\sin\left(x\right)+x\cos\left(x\right)\right)$

Step-by-step explanation

Problem to solve:

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

Rewriting the high order derivative

$\frac{d}{dx}\left(\frac{d}{dx}\left(x\cos\left(x\right)\right)\right)$
2

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\cos\left(x\right)$

$\frac{d}{dx}\left(\frac{d}{dx}\left(x\right)\cos\left(x\right)+x\frac{d}{dx}\left(\cos\left(x\right)\right)\right)$

Unlock this step-by-step solution!

Answer

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

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.57 seconds

Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!