Understanding Derivatives of Exponential Functions

The video tutorial explains how to find the derivative of an exponential function with base e using the chain rule. It begins with an introduction to the derivative formula and identifies the function and its components. The tutorial then demonstrates how to apply the chain rule, perform substitutions, and simplify the expression to arrive at the final result. The process involves factoring and simplifying the expression to present the derivative in its simplest form.

What is the derivative formula for e^u with respect to x?

• e^u * u'

• u * e^x

• e^x * x'

• u' * e^x

In the function f(x) = 14e^u, what is the expression for f'(x)?

• 14e^u * u'

• u' * 14e^x

• 14u * e^x

• e^u * 14x'

What is the common factor in the expression 3x^2 - 6?

• 2

• x

• 6

• 3

How is the expression 3 * 14 simplified in the final derivative?

• 36

• 42

• 28

• 56

What is the final simplified form of the derivative f'(x)?

• 42 * (x^2 - 2) * e^(x^3 - 6x)

• 14 * (x^2 - 2) * e^(x^3 - 6x)

• 42 * (x^2 - 6) * e^(x^3 - 2x)

• 14 * (x^2 - 6) * e^(x^3 - 2x)