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Math 101 Chapter 3: Differentiation
3.14 Derivative of the exponential function
3.16 Examples of rates of change
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3.15 Derivatives of hyperbolic functions
Example
The derivatives of the hyperbolic functions are
d
d
x
cosh
x
=
sinh
x
,
d
d
x
sinh
x
=
cosh
x
,
{{d}\over{dx}}\cosh x=\sinh x,\quad{{d}\over{dx}}\sinh x=\cosh x,
d
d
x
tanh
x
=
sech
2
x
.
{{d}\over{dx}}\tanh x={\hbox{sech}}^{2}x.
Solution.
From the definitions we have