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Find the higher order ($3$) derivative of $x\cos\left(x\right)$

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Solution

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Final answer to the problem

$-3\cos\left(x\right)+x\sin\left(x\right)$
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Step-by-step Solution

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  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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1

Find the ($1$) derivative

Learn how to solve differential calculus problems step by step online.

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

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Unlock the first 3 steps of this solution

Learn how to solve differential calculus problems step by step online. Find the higher order (3) derivative of xcos(x). Find the (1) derivative. Find the (2) derivative. Find the (3) derivative.

Final answer to the problem

$-3\cos\left(x\right)+x\sin\left(x\right)$

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Function Plot

Plotting: $-3\cos\left(x\right)+x\sin\left(x\right)$

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Got a different answer? Verify it!

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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
D□x
∫
∫◻
|◻|
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

How to improve your answer:

Similar Problems Solved

Find the derivative

$\frac{d^3}{dx^3}\left(x\cdot\cos\left(x\right)\right)$

Find the derivative

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

Find the derivative

$\frac{d^{\left(4\right)}}{dx^{\left(4\right)}}\left(x^4\cdot\ln\left(x\right)\right)$

Find the derivative

$\frac{d^{\left(7\right)}}{dx^{\left(7\right)}}\left(x^6\cdot\ln\left(x\right)\right)$

Find the derivative

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

Find the derivative

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

Find the derivative

$\frac{d^2}{dx^2}\left(x^3\right)$

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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