## d/dx (cosh x)

### To find the derivative of cosh x with respect to x, we can use the chain rule of differentiation

To find the derivative of cosh x with respect to x, we can use the chain rule of differentiation. Recall that the hyperbolic cosine function cosh x is defined as:

cosh x = (e^x + e^(-x))/2

Now, let’s differentiate it step by step:

First, let’s define u = e^x + e^(-x).

Taking the derivative of u with respect to x gives:

du/dx = d/dx (e^x + e^(-x))

Using the chain rule, we can see that du/dx = (e^x – e^(-x)), as the derivative of e^x is e^x, and the derivative of e^(-x) is -e^(-x).

Now, let’s find the derivative of cosh x with respect to x:

d/dx (cosh x) = d/dx [(e^x + e^(-x))/2]

Using the chain rule, we can write this as:

d/dx (cosh x) = (1/2) * du/dx

Substituting the value of du/dx, we get:

d/dx (cosh x) = (1/2) * (e^x – e^(-x))

Thus, the derivative of cosh x with respect to x is (e^x – e^(-x))/2.

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