checking the answer of integral of sqrt(tan(x)) by differentiation

TL;DR

This video provides a step-by-step explanation of how to differentiate the integral of square root of tangent X.

Transcript

okay so this is going to be my most difficult differentiation question so far all right we'll be differentiating this giant expression and I think some of you guys recognize what this is right this is the result that we got from the integral of square root of tangent X so you know after all the work we should end up with just a square root of tange... Read More

Key Insights

• 😑 The differentiation of the integral of square root of tangent X involves breaking down the expression into two terms and applying the chain rule.
• 📏 The derivatives of inverse hyperbolic tangent and square root of cotangent X are calculated using the chain rule and basic derivative rules.
• 😑 Common terms are canceled out to simplify the expression and obtain the final result.

Questions & Answers

Q: What is the approach taken to differentiate the integral of square root of tangent X?

The video breaks down the expression into two terms and applies the chain rule to differentiate each term individually. It then simplifies the expression and cancels out common terms to obtain the final result.

Q: What is the derivative of inverse hyperbolic tangent?

The derivative of inverse hyperbolic tangent is 1 over 1 minus the square of the inside function.

Q: How is the chain rule applied in differentiating the expression?

The chain rule is applied by differentiating the inside functions of both terms individually and multiplying them with the derivative of the outer function.

Q: How is the final expression simplified?

The final expression is simplified by canceling out common terms and factoring out common factors. This results in the expression 2 over tangent X plus cotangent X.

Summary & Key Takeaways

• The video demonstrates how to differentiate the integral of square root of tangent X by breaking it down into two terms and utilizing the chain rule.

• The first term involves differentiating the inverse hyperbolic tangent, while the second term involves differentiating the square root of cotangent X.

• By simplifying the expression and canceling out common terms, the final result is determined to be 2 over tangent X plus cotangent X.