Derivatives of Logarithmic Functions

This video tutorial covers derivatives of exponential and logarithmic functions, including e to the x, natural logs, and logarithmic differentiation. It explains the power rule, basic derivatives, and the chain rule. The tutorial also delves into advanced topics like logarithmic differentiation for complex functions and implicit differentiation, providing examples and formulas for each concept.

What is the derivative of e raised to the power of 2x?

• 2e^x

• e^2x

• e^x

• 2e^2x

How do you find the derivative of x raised to the power of a constant?

• Use the product rule

• Use the power rule

• Use implicit differentiation

• Use the chain rule

What is the derivative of e raised to the power of x squared?

• e^x^2

• x^2e^x

• 2xe^x

• 2xe^x^2

What is the derivative of the natural log of x?

• x^2

• x

• ln(x)

• 1/x

How do you find the derivative of ln(x^2)?

• 2x

• 2/x

• x^2

• 1/x

What is the derivative of log base 3 of 2x?

• 2/x ln(3)

• 1/x ln(3)

• 2/ln(3)

• ln(3)/x

What rule is used to find the derivative of x ln(x)?

• Quotient rule

• Chain rule

• Power rule

• Product rule

What is the derivative of x raised to the power of x?

• ln(x)

• x^x

• x^x (ln(x) + 1)

• x^x ln(x)

How do you differentiate a variable raised to another variable?

• Use implicit differentiation

• Use the chain rule

• Use the power rule

• Use logarithmic differentiation

What is the derivative of ln(ln(x))?

• ln(x)

• x ln(x)

• 1/x

• 1/x ln(x)