Differentiation of Exponential Functions

The video tutorial explains how to determine the derivative of a function using the chain rule. It starts by identifying the function and applying the chain rule to find the derivative of the exponent. The process involves calculating the derivative of the inner function and substituting it back into the main function. The tutorial concludes with the final expression for the derivative, emphasizing the use of hyperbolic functions and multiplication.

What is the initial function given in the problem?

• f(x) = 3e^(2 sinh(4x))

• f(x) = 2e^(3 sinh(4x))

• f(x) = 2e^(4 sinh(3x))

• f(x) = 4e^(3 sinh(2x))

Which rule is primarily used to find the derivative of the given function?

• Chain Rule

• Quotient Rule

• Product Rule

• Power Rule

What is the derivative of the inner function 3 sinh(4x)?

• 12 cosh(4x)

• 3 cosh(4x)

• 4 cosh(3x)

• 12 sinh(4x)

What is the value of u in the expression e^u for the given function?

• 3 cosh(4x)

• 4 cosh(3x)

• 4 sinh(3x)

• 3 sinh(4x)

What is the final expression for the derivative f'(x)?

• 12e^(3 sinh(4x)) sinh(4x)

• 24e^(3 sinh(4x)) cosh(4x)

• 12e^(4 sinh(3x)) cosh(4x)

• 24e^(4 sinh(3x)) cosh(3x)

What operation is performed to simplify the final expression for f'(x)?

• Addition of constants

• Subtraction of constants

• Division of constants

• Multiplication of constants