# Same Derivatives Implies Same Functions? | Summary and Q&A

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July 19, 2018
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blackpenredpen
Same Derivatives Implies Same Functions?

## TL;DR

This video explains how to simplify a trigonometric expression using calculus, ultimately demonstrating that two trig expressions are equal.

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### Q: What is the initial trig expression being simplified in the video?

The initial trig expression being simplified is the inverse tangent of X minus the square root of x squared plus 1.

### Q: How is the chain rule used in the simplification process?

The chain rule is applied to find the derivative of the inner function in the expression, which involves multiplying by the derivative of the inside function.

### Q: How are algebraic manipulations used to simplify the expression?

Algebraic manipulations such as expanding squares and combining like terms are used to simplify the expression and rewrite it in a simpler form.

### Q: How does the video demonstrate that the simplified expression is equal to a known trig identity?

By picking a value for X and plugging it into both the simplified expression and the known trig identity, the video shows that they produce the same result, proving their equality.

## Summary & Key Takeaways

• The video demonstrates the step-by-step process of simplifying a trig expression using calculus.

• The chain rule and algebraic manipulations are applied to simplify the expression.

• The simplified expression is then compared to a known trig identity, showing that they are equal.