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.

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Q:
## What Is the Derivative of Cosecant?

A: The derivative of cosecant(x) with respect to x is -cot(x)csc(x). Here, cot(x) is defined as 1/tan(x), and csc(x) is the notation normally used for the cos... Full Answer >Filed Under: -
Q:
## What Is the Antiderivative of Sec(x)?

A: The antiderivative of sec(x) is equal to ln |sec(x) + tan(x)| + C, where C represents a constant. This antiderivative, also known as an integral, can be so... Full Answer >Filed Under: -
Q:
## What Is the Derivative of E^-X?

A: The derivative of e-x is -e-x. The derivative of e-x is found by applying the chain rule of derivatives and the knowledge that the derivative of ex is alwa... Full Answer >Filed Under: -
Q:
## What Is the Derivative of the Square Root of X?

A: The derivative of the square root of x is one-half times one divided by the square root of x. The square root of x is equal to x to the power of one-half. Full Answer >Filed Under: