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# Find the derivative of $2x^3\mathrm{tanh}\left(\frac{1}{x^2}\right)$

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##  Final answer to the problem

$6x^{2}\mathrm{tanh}\left(\frac{1}{x^2}\right)-4\mathrm{sech}\left(\frac{1}{x^2}\right)^2$
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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
Can't find a method? Tell us so we can add it.
1

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$2\frac{d}{dx}\left(x^3\mathrm{tanh}\left(\frac{1}{x^2}\right)\right)$

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

$2\frac{d}{dx}\left(x^3\mathrm{tanh}\left(\frac{1}{x^2}\right)\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of 2x^3tanh(1/(x^2)). 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=. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Taking the derivative of hyperbolic tangent.

##  Final answer to the problem

$6x^{2}\mathrm{tanh}\left(\frac{1}{x^2}\right)-4\mathrm{sech}\left(\frac{1}{x^2}\right)^2$

##  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

SnapXam A2

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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
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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