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# Find the derivative of $\tan\left(e^x-e^{-x}\right)$

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##  Final answer to the problem

$\left(e^x+e^{-x}\right)\sec\left(e^x-e^{-x}\right)^2$
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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
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1

The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if ${f(x) = tan(x)}$, then ${f'(x) = sec^2(x)\cdot D_x(x)}$

$\frac{d}{dx}\left(e^x-e^{-x}\right)\sec\left(e^x-e^{-x}\right)^2$

Learn how to solve problems step by step online.

$\frac{d}{dx}\left(e^x-e^{-x}\right)\sec\left(e^x-e^{-x}\right)^2$

Learn how to solve problems step by step online. Find the derivative of tan(e^x-e^(-x)). The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Applying the derivative of the exponential function.

##  Final answer to the problem

$\left(e^x+e^{-x}\right)\sec\left(e^x-e^{-x}\right)^2$

##  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

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