Question

find $D_{x} y$. $$y=\tanh (\cot x)$$

Name: Problem 35, Chapter 6: Calculus
Uploaded: 2021-06-17T05:11:49-08:00
Duration: 1 min 1 s
Channel: Tyler Moulton
Description: find Dx y. y=tanh(cotx)

   find $D_{x} y$.
$$y=\tanh (\cot x)$$

Calculus

Dale Varberg, Edwin… 9th Edition

Chapter 6, Problem 35

Instant Answer

Solved by Expert Tyler Moulton

06/17/2021

Step 1

The derivative of $\tanh x$ is $\operatorname{sech}^{2} x$. Show more…

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find $D_{x} y$. $$y=\tanh (\cot x)$$

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Key Concepts

Chain Rule

The chain rule is a fundamental technique in differentiation used for finding the derivative of a composite function. When a function is composed of two or more functions, the derivative is obtained by multiplying the derivative of the outer function evaluated at the inner function by the derivative of the inner function.

Differentiation of Hyperbolic Functions

Hyperbolic functions, such as tanh(x), have specific derivatives that are used in calculus. The derivative of tanh(x) is given by sech²(x), and this formula is crucial when applying differentiation rules to functions involving hyperbolic expressions.

Differentiation of Trigonometric Functions

Trigonometric functions also have well-established derivative formulas. In this context, the cotangent function, cot(x), is differentiated using its standard formula, where the derivative is -csc²(x). This concept is important when dealing with composite functions that include trigonometric components.

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