Find the Derivative of y = arctan(x/4) - 1/(2(x^2 + 16))

TL;DR

Find derivative of arctan function by simplifying expression step by step.

Transcript

we have to find the derivative of this function so the derivative of the arctan function so DDX of arctangent of X is equal to 1 over 1 plus x squared however here we have the arc tangent of x over 4 so might be beneficial to first start by rewriting this problem as follows so arctangent of 1/4 X this way when you take the derivative and use the ch... Read More

Key Insights

• 😑 Rewriting expressions can make differentiation easier.
• 📏 Understanding the chain rule simplifies finding derivatives.
• 🦻 Bringing the bottom piece up before differentiation can aid in the process.
• ❓ Simplifying the final answer is crucial for clarity and accuracy.
• 🛀 Steps shown illustrate the process of finding the derivative of arctan function effectively.
• 📏 Differentiation involves application of derivative rules like chain rule and simplification techniques.
• ✋ Knowing when to stop simplification is a practical decision in mathematical solutions.

Questions & Answers

Q: How do you simplify finding the derivative of the arctan function?

To simplify finding the derivative of arctan function, rewrite the expression to arctan(1/4x) and then use the chain rule for differentiation following the steps shown in the video.

Q: Why is it beneficial to rewrite the expression for easier differentiation?

Rewriting the expression as arctan(1/4x) makes it easier to differentiate because the chain rule can be applied directly to 1/4x, simplifying the process and reducing errors.

Q: When is it a good idea to bring the bottom piece up before differentiating a fraction?

It is a good idea to bring the bottom piece up before differentiating a fraction when there is a number on top, as shown in the video, to make the differentiation process smoother.

Q: Why is simplifying the final answer important in finding the derivative?

Simplifying the final answer is important in finding the derivative to present a more concise and clear solution, reducing complex fractions and making the result more understandable.

Summary & Key Takeaways

• Derivation of arctan function involves rewriting the expression for easier differentiation.

• Use chain rule to find derivative of 1/4x, simplifying the process.

• Steps shown to simplify the final answer for the derivative.