Question

What is the derivative of sech u with respect to x?

Answer 1

`\displaystyle (dy)/(dx) = -u'sech(u)tanh(u)`

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Derivative Rule [Chain Rule]:
`\displaystyle (d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)`

Explanation:

*Note:

This is a known derivative (apply trigonometric differentiation).

Step 1: Define

Identify

`\displaystyle y = sech(u)`

Step 2: Differentiate

1. Hyperbolic Differentiation [Derivative Rule - Chain Rule]:
   `\displaystyle y' = -u'sech(u)tanh(u)`

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation