Derivatives of Exponential and Logarithmic Functions

This video tutorial covers the derivatives of exponential and logarithmic functions. It begins with an introduction to the concept of derivatives, focusing on the derivative of e^x, which is shown to be e^x itself. The tutorial then applies the chain rule to find derivatives of functions in the form of e^u and a^u. It also explains how to derive the formula for the derivative of ln(x) by exponentiating both sides and using the chain rule. Finally, the video discusses the derivatives of logarithmic functions with bases other than e, using the change of base rule.

What is the slope of the function y = e^x at x = 0?

• Undefined

• e

• 1

• 0

What does the derivative of y = e^x simplify to?

• 1

• x * e^x

• x

• e^x

What is the result of differentiating e^x?

• e^x

• 1

• e

• x

Using the chain rule, what is the derivative of e^u?

• u * e^u

• e^u

• e^(u+1)

• e^u * du/dx

How can the derivative of a^x be expressed using e?

• x * ln(a)

• a^(e^x)

• e^(x * ln(a))

• a^x * ln(a)

What is the derivative of a^u using the chain rule?

• a^u * ln(a) * du/dx

• u * ln(a)

• a^(u+1)

• a^u

What is the derivative of ln(x)?

• 1/x

• ln(x)

• x/ln(x)

• 1

What is the derivative of ln(u) using the chain rule?

• u/ln(u)

• 1/u * du/dx

• ln(u) * du/dx

• 1/u

What is the derivative of the common logarithm function log(x)?

• ln(10)/x

• 1/ln(10)

• 1/x

• 1/(x * ln(10))

What is the derivative of log base a of u?

• 1/u

• ln(a)/u

• 1/(u * ln(a))

• 1/(u * ln(a)) * du/dx