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# Find the derivative of $3\sin\left(x-2\right)\mathrm{sinh}\left(x\right)$

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##  Final answer to the problem

$3\cos\left(x-2\right)\mathrm{sinh}\left(x\right)+3\sin\left(x-2\right)\mathrm{cosh}\left(x\right)$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• 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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The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$3\frac{d}{dx}\left(\sin\left(x-2\right)\mathrm{sinh}\left(x\right)\right)$

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

$3\frac{d}{dx}\left(\sin\left(x-2\right)\mathrm{sinh}\left(x\right)\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of 3sin(x-2)sinh(x). The derivative of a function multiplied by a constant 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=\sin\left(x-2\right) and g=\mathrm{sinh}\left(x\right). The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. The derivative of a sum of two or more functions is the sum of the derivatives of each function.

##  Final answer to the problem

$3\cos\left(x-2\right)\mathrm{sinh}\left(x\right)+3\sin\left(x-2\right)\mathrm{cosh}\left(x\right)$

##  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

SnapXam A2

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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.