Understanding the Derivative of Cotangent

The video tutorial provides a step-by-step proof that the derivative of cotangent x with respect to x equals negative cosecant squared x. It begins by rewriting cotangent x using trigonometric identities, then applies the quotient rule to find the derivative of cosine x over sine x. The tutorial continues by simplifying the expression using trigonometric identities and algebraic manipulation, ultimately concluding with the final proof that the derivative of cotangent x is negative cosecant squared x.

What is the initial step in proving the derivative of cotangent x?

• Using the product rule

• Directly differentiating cotangent x

• Applying the chain rule

• Rewriting cotangent x using trigonometric identities

Which rule is used to find the derivative of cosine x over sine x?

• Quotient rule

• Chain rule

• Product rule

• Power rule

What is the derivative of cosine x?

• Negative cosine x

• Cosine x

• Negative sine x

• Sine x

What is the derivative of sine x?

• Sine x

• Negative cosine x

• Cosine x

• Negative sine x

How can sin^2 x be rewritten?

• 1 + cos^2 x

• sin x^2

• cos^2 x

• 1 - cos^2 x

What identity is used to simplify sin^2 x + cos^2 x?

• Half angle identity

• Double angle identity

• Sum of angles identity

• Pythagorean identity

What does the expression -1 / sin^2 x simplify to?

• Negative cosecant squared x

• Negative secant squared x

• Negative tangent squared x

• Negative cotangent squared x

What is the final result of the derivative of cotangent x?

• Negative cosecant squared x

• Negative secant squared x

• Negative sine x

• Negative cosine x