Question #e4cab

1 Answer

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)