Using the chain rule to take the derivative of an exponential equation

The video tutorial explains how to find the derivative of an exponential function using the chain rule. It begins by defining the inside function as 5x and discusses different notations for derivatives, such as g of x and du over dx. The tutorial then applies the chain rule, taking the derivative of the outside function e to the x and multiplying it by the derivative of the inside function, resulting in 5 times e to the 5x.

What is an example of an inside function in an exponential function?

• 3x

• 9x

• 5x

• 7x

Which notation can be used to represent the derivative of the inside function?

• f'(x)

• h'(x)

• k'(x)

• g'(x)

What is the derivative of the outside function e^x?

• e^x

• ex

• xe

• x^e

How do you apply the chain rule to find the derivative of a composite function?

• Add the derivatives of both functions

• Multiply the derivatives of both functions

• Subtract the derivative of the inside function from the outside function

• Divide the derivative of the outside function by the inside function

What is the final derivative of the function e^(5x)?

• 5x * e^(5x)

• e^(5x)

• 5e^(5x)

• x * e^(5x)