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

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## Final Answer

$\sec\left(e^x-e^{-x}\right)^2\left(e^x+e^{-x}\right)$
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## Step-by-step Solution

Problem to solve:

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

Specify the solving method

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 ${f'(x) = sec^2(x)\cdot D_x(x)}$

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

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

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

Learn how to solve differential calculus 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 (-1) is equal to the constant times the derivative of the function. Applying the derivative of the exponential function.

## Final Answer

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

### Explore different ways to solve this problem

Find the derivativeProduct ruleQuotient ruleLogarithmic differentiation
SnapXam A2
Answer Assistant

Go!
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

### Useful tips on how to improve your answer:

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

### Main topic:

Differential Calculus

~ 0.08 s