Find the Derivative dy/dx using Logarithmic Differentiation | Summary and Q&A

TL;DR

This video explains how to find the derivative of a function using logarithmic differentiation.

Key Insights

• 🧑‍💻 Logarithmic differentiation involves taking the natural log of a function, simplifying it using logarithmic properties, and then finding the derivative.
• 📏 The power rule and product rule for logarithms are important tools in this process.
• 😑 The final result is a complex expression that can be simplified further by substituting the original function back in.
• 😑 Logarithmic differentiation is a useful technique for finding the derivative of functions involving exponential or complicated expressions.
• ✊ This method is particularly helpful when using the quotient rule or when the function involves products or powers that would be challenging to differentiate directly.
• 😑 Logarithmic differentiation can be time-consuming and may result in long, complicated expressions.
• 😑 Check your work by plugging the original function back into the expression if possible.

Transcript

in this video we're going to find d y d x using logarithmic differentiation so the process of logarithmic differentiation works as follows the first step is we take the natural log on both sides so ln of y equals ln of all of this so all of this whenever you have a cube root you can just take all of this and write it to the one third power it's 1 o... Read More

Questions & Answers

Q: What is the first step in logarithmic differentiation?

The first step is to take the natural log of both sides of the equation.

Q: How are properties of logarithms used in this process?

Properties like the power rule and product rule for logarithms are used to simplify the expression before taking the derivative.

Q: How can the derivative of the inside function be found?

The derivative of the inside function can be found using the power rule for derivatives, where the exponent is multiplied by the original function and the exponent is reduced by one.

Q: Can the original function be substituted back into the expression?

Yes, the original function can be substituted back into the expression to simplify it further, if desired.

Summary & Key Takeaways

• Logarithmic differentiation involves taking the natural log of a function and then using properties of logarithms to simplify it.

• The derivative of the function is then found by applying the power rule and product rule for logarithms.

• The final result is a complicated expression that can be simplified further by substituting the original function back in.