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# Find the derivative of $8x\sin\left(x\right)\cos\left(x\right)$

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##  Final Answer

$8\sin\left(x\right)\cos\left(x\right)+8x\cos\left(x\right)^2-8x\sin\left(x\right)^2$
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##  Step-by-step Solution 

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The derivative of a function multiplied by a constant ($8$) is equal to the constant times the derivative of the function

$8\frac{d}{dx}\left(x\sin\left(x\right)\cos\left(x\right)\right)$

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

$8\frac{d}{dx}\left(x\sin\left(x\right)\cos\left(x\right)\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of 8xsin(x)cos(x). The derivative of a function multiplied by a constant (8) is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\sin\left(x\right)\cos\left(x\right). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sin\left(x\right) and g=\cos\left(x\right). The derivative of the linear function is equal to 1.

##  Final Answer

$8\sin\left(x\right)\cos\left(x\right)+8x\cos\left(x\right)^2-8x\sin\left(x\right)^2$

##  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 8x using the product ruleFind derivative of 8x using the quotient ruleFind derivative of 8x using logarithmic differentiation

SnapXam A2

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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: 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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