Understanding Derivatives of Logarithms

The video tutorial explains how to find the derivative of a logarithm with an arbitrary base using the change of base formula. It starts by reviewing the derivative of the natural log and then introduces the change of base formula to express a logarithm with a different base in terms of natural logs. The tutorial demonstrates how to apply this formula to simplify the derivative calculation, ultimately showing that the derivative of log base b of x is 1 over the natural log of b times 1/x.

What is the derivative of the natural logarithm of x with respect to x?

• x^2

• 1/x

• ln(x)

• x

Which formula allows us to convert a logarithm with any base to a natural logarithm?

• Product Rule

• Quotient Rule

• Power Rule

• Change of Base Formula

How can log base b of x be expressed using natural logarithms?

• ln(b) / ln(x)

• ln(x) / ln(b)

• ln(x) * ln(b)

• ln(x) + ln(b)

What is the derivative of ln(x) with respect to x?

• x

• ln(x)

• x^2

• 1/x

When simplifying the derivative of log base b of x, what can be factored out as a constant?

• 1/x

• 1/ln(b)

• x

• ln(x)

What is the derivative of log base 5 of x with respect to x?

• x/ln(5)

• 1/(ln(5) * x)

• ln(5)/x

• 1/(5x)