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Find the derivative using the product rule $\frac{d}{dx}\left(\tan\left(e^x-e^{-x}\right)\right)$

Step-by-step Solution

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Final Answer

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

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

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

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

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Learn how to solve differential equations problems step by step online. Find the derivative using the product rule d/dx(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. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=-1 and g=e^{-x}. The derivative of the constant function (-1) is equal to zero.

Final Answer

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

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Find the derivativeFind derivative of tan(e^x+-1e^-1x) using the quotient ruleFind derivative of tan(e^x+-1e^-1x) using logarithmic differentiation

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

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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

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Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

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