What is the derivative of cosh(x)?

1 Answer
Nico Ekkart
Dec 19, 2014

The definition of cosh(x) is (e^x + e^-x)/2, so let's take the derivative of that:

d/dx ((e^x + e^-x)/2)
We can bring 1/2 upfront.
1/2(d/dxe^x + d/dxe^-x)
For the first part, we can just use the fact that the derivative of e^x = e^x:
1/2(e^x + d/dxe^-x)
For the second part, we can use the same definition, but we also have to use the chain rule. For this, we need the derivative of -x, which is simply -1:
1/2(e^x + (-1)e^-x)
=1/2(e^x - e^-x)
=(e^x-e^-x)/2
=sinh(x) (definition of sinh).

And that's you're derivative.
Hope it helped.

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