Take the derivative of a function by taking the log of both sides

The video tutorial explains how to use logarithmic differentiation to find the derivative of a function with a base other than e. It begins by discussing the limitations of directly differentiating such functions and introduces the concept of taking the natural logarithm of both sides to simplify the process. The tutorial then demonstrates how to apply the power rule and other derivative rules to complete the derivation, emphasizing the importance of understanding constants like the natural logarithm of a number.

Why is it necessary to take the natural logarithm of both sides when dealing with a base three exponent?

• Because it makes the function linear

• Because it eliminates the need for the chain rule

• Because it simplifies the derivative process

• Because it changes the base to e

What is the role of the natural logarithm of a number in the derivative process?

• It becomes zero

• It is treated as a constant

• It acts as a variable

• It is ignored

After taking the natural logarithm, what is the next step in finding the derivative?

• Change the base to e

• Bring down the exponent

• Apply the chain rule

• Multiply by the original function

How do you isolate dy/dx in the final step of the derivative process?

• Add the natural logarithm

• Multiply by y

• Divide by x

• Subtract the exponent

What is the final expression for dy/dx in terms of x and y?

• Ln(3) * 15x^2 * y

• Ln(3) * 5x^3 * y

• Ln(3) * 5x^2 * y

• Ln(3) * 15x^3 * y