Derivatives of Hyperbolic Functions

This video tutorial covers the derivatives of hyperbolic functions, including hyperbolic sine, cosine, tangent, cosecant, secant, and cotangent. It provides a proof for the derivative of hyperbolic sine and offers practice problems to reinforce learning. The video also explores derivatives involving natural logarithms of hyperbolic functions, using rules like the product, quotient, and chain rules.

What is the derivative of the hyperbolic sine function?

• Hyperbolic secant

• Negative hyperbolic sine

• Hyperbolic cosine

• Hyperbolic tangent

How does the derivative of hyperbolic cosine differ from that of regular cosine?

• It is negative cosine

• It is hyperbolic tangent

• It is positive hyperbolic sine

• It is negative hyperbolic sine

What is the derivative of hyperbolic tangent?

• Hyperbolic cotangent

• Negative hyperbolic tangent

• Hyperbolic cosecant

• Hyperbolic secant squared

Which rule is used to differentiate hyperbolic sine of a function of x?

• Chain rule

• Quotient rule

• Power rule

• Product rule

What is the derivative of hyperbolic cosine of x cubed?

• 3x cubed hyperbolic sine of x cubed

• 3x cubed hyperbolic cosine of x cubed

• 3x squared hyperbolic cosine of x cubed

• 3x squared hyperbolic sine of x cubed

What is the derivative of hyperbolic secant x to the fourth?

• Negative 4x cubed hyperbolic secant x to the fourth times hyperbolic tangent x to the fourth

• 4x cubed hyperbolic secant x to the fourth times hyperbolic tangent x to the fourth

• Negative 4x cubed hyperbolic tangent x to the fourth

• 4x cubed hyperbolic tangent x to the fourth

Which rule is applied when differentiating a product of functions?

• Power rule

• Chain rule

• Quotient rule

• Product rule

What is the derivative of ln(hyperbolic sine of x)?

• Hyperbolic tangent of x

• Hyperbolic cotangent of x

• Hyperbolic secant of x

• Hyperbolic cosecant of x

What is the derivative of ln(hyperbolic cosine of x squared)?

• 2x times hyperbolic cosecant of x squared

• 2x times hyperbolic cotangent of x squared

• 2x times hyperbolic secant of x squared

• 2x times hyperbolic tangent of x squared

Which rule is used to differentiate natural logarithms of hyperbolic functions?

• Quotient rule

• Product rule

• Chain rule

• Power rule