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

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Answer:

[tex]\displaystyle \frac{dy}{dx} = -u'sech(u)tanh(u)[/tex]

General Formulas and Concepts:

Calculus

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

*Note:

This is a known derivative (apply trigonometric differentiation).

Step 1: Define

Identify

[tex]\displaystyle y = sech(u)[/tex]

Step 2: Differentiate

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

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

Unit: Differentiation

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