The-Organic-Chemistry-Tutor
This video teaches how to find derivatives using inverse hyperbolic functions using various formulas such as the derivative of inverse hyperbolic sine, cosine, tangent, cosecant, and cotangent functions. The video provides several examples to demonstrate how to apply the power rule and chain rule to find the derivative, including finding the derivative of an expression involving a product rule problem with six times the inverse hyperbolic sine of 3x and minus two square root one plus 9x squared. The YouTuber applies the power rule and the derivative 18x to get negative 18x over the square root of one plus 9x squared and simplifies the expression to get six inverse hyperbolic sine of 3x, allowing viewers to derive the derivative of inverse hyperbolic functions.
In this section, we learned about how to find the derivative of inverse hyperbolic functions using various formulas. These formulas include the derivative of inverse hyperbolic sine, cosine, tangent, cosecant, and cotangent functions. We also worked on practice problems using these formulas to find the derivative of functions with inverse hyperbolic functions. For example, we found the derivative of the inverse hyperbolic sine function of 4X and the inverse hyperbolic tangent function of the square root of x.
In this section, the video explains how to find derivatives using inverse hyperbolic functions with examples of finding the derivative of inverse hyperbolic tangent function of the square root of x and the inverse hyperbolic cosecant function of x raised to the third power. The video also demonstrates how to find the derivative of an expression involving a product rule problem with 6 times the inverse hyperbolic sine of 3x and minus 2 square root 1 plus 9x squared. The video explains the formula for inverse hyperbolic cosecant function and how to apply the power rule and chain rule to find the derivative.
In this section, the YouTuber starts by differentiating the second part of a given equation using the formula for the derivative of inverse sine, U Prime over the square root of U squared plus 1. With U being 3x and U Prime being 3, this is multiplied by 3/ the square root of 3x squared plus one. After rewriting the expression, the YouTuber applies the power rule and the derivative 18x to get negative 18x over the square root of 1 plus 9x squared. Simplifying the expression, the YouTuber then applies the addition property of 0 to derive the answer of six inverse hyperbolic sine of 3x, allowing viewers to derive the derivative of inverse hyperbolic functions.
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