The-Organic-Chemistry-Tutor
The video covers the topic of finding derivatives of hyperbolic functions using various rules such as the chain rule and the product rule. The derivatives of hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, and cotangent are explained using the derivative rules. The speaker also demonstrates examples of finding the derivatives of hyperbolic functions and natural logarithms of hyperbolic functions. The video highlights the similarities between the rules used in finding derivatives of hyperbolic functions and those used for other functions.
In this section, the focus is on the derivatives of hyperbolic functions. The derivative of hyperbolic sine is equal to hyperbolic cosine, and the derivative of hyperbolic cosine is hyperbolic sine. The derivative of hyperbolic tangent is hyperbolic secant squared, while the derivative of hyperbolic cosecant x is negative cosecant or hyperbolic cosecant times hyperbolic cotangent of x. The derivative of hyperbolic secant x is negative hyperbolic secant times hyperbolic tangent, and the derivative of cotangent is negative cosecant squared. By using the derivative rules, one can prove these derivatives. In practice, differentiating hyperbolic sine of 4x gives 4 hyperbolic cosine of 4x, and differentiating hyperbolic cosine of x cubed gives hyperbolic sine.
In this section, the process of finding the derivatives of various hyperbolic functions is shown through examples and different rules, such as the chain rule and the product rule, are utilized. These rules are similar to those used in finding the derivatives of other functions. The examples include finding the derivative of hyperbolic sine and hyperbolic cosine of different expressions of X, as well as finding the derivative of natural logarithms of hyperbolic sine and hyperbolic cosine of different expressions of X. The final answers include hyperbolic cotangent and hyperbolic tangent of different expressions of X.
In this section, the speaker discusses how to find derivatives of hyperbolic functions using the product rule, quotient rule, and chain rule. The speaker explains that the hyperbolic functions are defined in terms of exponential functions, so the derivative of hyperbolic functions can be found by using rules of exponential functions. The speaker demonstrates with examples of hyperbolic sine, cosine, tangent functions, showing how to use each of the three rules to find their derivatives.
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