Differentiating Logarithmic and Exponential Functions

This video tutorial covers logarithmic differentiation, starting with natural log functions and extending to regular log functions with different bases. It explains how to differentiate exponential functions using both equations and logarithmic differentiation. The tutorial includes practice examples and explores advanced applications of logarithmic differentiation for complex functions. It concludes with a discussion on the properties of logarithms and their applications in solving differentiation problems.

What is the derivative of ln(x^2 - 5x)?

• (2x - 5) / (x^2 - 5x)

• 2x - 5

• 1 / (x^2 - 5x)

• x^2 - 5x

What is the derivative of ln(x)?

• x ln(x)

• x

• 1/x

• ln(x)

How do you differentiate log base a of a variable u?

• u' / u

• a^u

• ln a / u

• u' / (u ln a)

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

• e^(5x)

• e^(5x) + 5

• 5e^(5x)

• 5x e^(5x)

How do you differentiate an exponential function with a base other than e?

• a^u * u'

• u' * ln a

• a^u * ln a

• a^u * u' * ln a

Using logarithmic differentiation, what is the derivative of x^x?

• ln(x^x)

• x^x ln x

• x^(x-1)

• x^x (ln x + 1)

What is the derivative of 5^x?

• 5^x ln 5

• x 5^x

• 5^x

• ln(5^x)

Which property of logarithms allows you to separate ln(a * b) into two terms?

• ln(a) * ln(b)

• ln(a) + ln(b)

• ln(a) - ln(b)

• ln(a / b)

Which rule is used when differentiating a product of two functions?

• Quotient Rule

• Chain Rule

• Product Rule

• Power Rule

What is the derivative of ln(a/b)?

• ln(a) + ln(b)

• a/b

• b/a

• ln(a) - ln(b)