Problems on Derivatives of Logarithmic Function Part 6 - Derivatives - Diploma Maths - II

TL;DR

• Learn how to find derivatives of logarithmic functions through examples 13 and 14.

Transcript

click the bell icon to get latest videos from equator hello friends in this video we are going to continue how to find the derivative of logarithmic function by solving problem number 13 and 14 let us start in problem number 13 we have find dy by DX if log to the base 10 of log X to the base 10 is equal to Y Y can be considered as log of log X to t... Read More

Key Insights

• 📏 Understanding composite function rule in differentiation.
• 🈸 Application of logarithmic properties in finding derivatives.
• ❓ Utilizing trigonometric functions in differentiation.
• 📏 Appreciation of chain rule for solving problems.
• ❓ Importance of simplification in derivative analysis.
• ❓ Enhancing skills in finding derivatives through examples.
• ❓ Relationship between logarithmic and trigonometric functions.

Questions & Answers

Q: How do you find the derivative of log(logX) in problem 13?

To find dy/dx for Y = log(logX), apply composite function rule and simplify to obtain the derivative as 1/(X logX).

Q: What is the approach to differentiating Y = log(sinX) in problem 14?

By applying the chain rule and simplifying, the derivative of Y = log(sinX) is found to be (X logX cosX - log(sinX)) / X logX^2.

Summary & Key Takeaways

• Derivative of log(logX) where Y = log(logX).

• Utilize composite function rule to simplify and differentiate.

• Final answers for both problems involve log and trigonometric functions.