Understanding the Derivative of Tangent X

The video tutorial demonstrates the proof that the derivative of tangent x with respect to x is equal to secant squared x. It begins by rewriting tangent x using the sine and cosine identity, then applies the quotient rule to find the derivative. The process involves simplifying the expression and using trigonometric identities to arrive at the final proof, showing that the derivative of tangent x is indeed secant squared x.

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

• Using the Pythagorean identity

• Applying the chain rule

• Rewriting tangent x using the quotient identity

• Using the product rule

Which rule is applied to find the derivative of sin x over cosine x?

• Product rule

• Chain rule

• Quotient rule

• Power rule

What is the derivative of sin x?

• cosine x

• sine x

• secant x

• tangent x

How is cosine squared x rewritten in the simplification process?

• sine 2x

• sine x

• cosine 2x

• cosine x

What is the derivative of cosine x?

• Cosine x

• Negative cosine x

• Negative sine x

• Sine x

What identity is used to simplify the expression to 1/cosine x?

• Sum identity

• Reciprocal identity

• Pythagorean identity

• Quotient identity

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

• Secant x

• Secant squared x

• Cosine x

• Sine x

Which of the following is equal to 1/cosine x?

• Sine x

• Tangent x

• Cotangent x

• Secant x