Q:
# What is the derivative of cosh x?

**The derivative of cosh(x) with respect to x is sinh(x).** One can verify this result using the definitions cosh(x) = (e^x + e^(-x))/2 and sinh(x) = (e^x - e^(-x))/2.

By definition, the derivative of e^x with respect to x is e^x. The derivative of e^(-x) with respect to x is -e^(-x). Therefore, d(cosh(x))/dx = (e^x - e^(-x))/2 = sinh(x). The graph of y = cosh(x) is a hyperbola with a local minimum at (0,1). The graph of y = sinh(x) is the slope of this hyperbola. This graph increases as x increases, and it has a point of inflection at the origin.

Learn more about Calculus-
Q:
## What is the precise definition of a limit in calculus?

A: The definition of a limit in calculus is the value that a function gets close to but never surpasses as the input changes. Limits are one of the most impor... Full Answer >Filed Under: -
Q:
## What did Sir Isaac Newton do with math?

A: Newton was one of two people credited with the creation of calculus, but even though he developed his ideas first, he did not get them printed first. A Ger... Full Answer >Filed Under: -
Q:
## How are decimals written in expanded form?

A: A decimal number is written in expanded form by multiplying each individual number by the value of the decimal place that it occupies. Expanded form is rar... Full Answer >Filed Under: -
Q:
## How do you find the value of arctan 0?

A: Arctan, like arcsin and arccos, is an inverse trignometric function that determines at what angle a given fraction occurs. Inverse trigonometric functions ... Full Answer >Filed Under: