Derivatives of Inverse Hyperbolic Functions

This video tutorial covers the derivatives of inverse hyperbolic functions, providing formulas and practice problems for each function. It includes detailed solutions for derivatives of inverse hyperbolic sine, cosine, tangent, cosecant, and a final problem that combines these concepts. The tutorial aims to enhance understanding of these derivatives through step-by-step examples.

What is the derivative of the inverse hyperbolic sine function of a variable U?

• U Prime over the square root of U squared plus 1

• Negative U Prime over the absolute value of U

• U Prime over the square root of U squared minus 1

• U Prime over 1 minus U squared

Which formula represents the derivative of the inverse hyperbolic cosine function?

• Negative U Prime over the absolute value of U

• U Prime over 1 minus U squared

• U Prime over the square root of U squared minus 1

• U Prime over the square root of U squared plus 1

How is the derivative of the inverse hyperbolic tangent function expressed?

• U Prime over the square root of U squared plus 1

• U Prime over the square root of U squared minus 1

• U Prime over 1 minus U squared

• Negative U Prime over the absolute value of U

What is the derivative of the inverse hyperbolic sine function of 4X?

• 4 over the square root of 16x squared plus 1

• 4 over the square root of 4x squared minus 1

• 4 over 1 minus 16x squared

• Negative 4 over the absolute value of 4x

In the example of finding the derivative of the inverse hyperbolic cosine of X cubed, what is U Prime?

• 3x squared

• X cubed

• 3x

• X squared

What is the derivative of the inverse hyperbolic tangent function of the square root of x?

• 1 over 2 square root x times X

• 1 over 2 square root x times 1 minus X

• 1 over 2 square root x minus X

• 1 over 2 square root x plus X

When using the chain rule for the inverse hyperbolic cosecant function raised to the third power, what is the first step?

• Differentiate the inside part

• Multiply by the derivative of the inside part

• Differentiate as if it's X cubed

• Use the product rule

What is the derivative of the inverse hyperbolic cosecant function of x raised to the third power?

• Negative 3 times inverse hyperbolic cosecant of x squared over the absolute value of x times the square root of 1 plus x squared

• 3 times inverse hyperbolic cosecant of x over the absolute value of x times the square root of 1 plus x squared

• 3 times inverse hyperbolic cosecant of x squared over the absolute value of x times the square root of 1 plus x squared

• Negative 3 times inverse hyperbolic cosecant of x over the absolute value of x times the square root of 1 plus x squared

In the final example, what rule is used to find the derivative of the expression involving inverse hyperbolic sine?

• Quotient rule

• Chain rule

• Product rule

• Power rule

What is the final derivative of the expression Y = 6x times the inverse hyperbolic sine of 3x minus 2 square root of 1 plus 9x squared?

• 6x inverse hyperbolic sine of 3x

• 6 inverse hyperbolic sine of x

• 6x inverse hyperbolic sine of x

• 6 inverse hyperbolic sine of 3x