Question

Question #e4cab

Answer 1

`d/dx(cosh(x))=sinh(x)`

Explanation:

A given value but the proof is that
`sinh(x)` is given as `(e^x-e^-x)/2`
And `cosh(x)=(e^x+e^-x)/2`
And the derivative is `1/2(d/dx)(e^x)+(1/2)(d/dx)(e^-x)`
The derivative of any `e^x` is `e^x` also the `-x` brings down the negative because of the chain rule
You get `1/2e^x+1/2e^-x(-1)`
`1/2e^x-1/2e^-x`
or `(e^x-e^-x)/2`
so `d/dx(cosh(x))=sinh(x)`