Understanding the Derivative of Secant Function

The video tutorial provides a step-by-step proof that the derivative of secant x with respect to x is secant x times tangent x. It begins by rewriting secant x using the reciprocal identity, then applies the quotient rule to find the derivative. The process involves simplifying the expression and concludes with a final proof, demonstrating that the derivative of secant x is indeed secant x times tangent x.

What is the derivative of secant x with respect to x?

• Secant x times tangent x

• Secant x times sine x

• Sine x times cosine x

• Tangent x times cosine x

How is secant x rewritten using the reciprocal identity?

• One over cosine x

• One over sine x

• Sine x over cosine x

• Cosine x over sine x

What rule is applied to find the derivative of one over cosine x?

• Power rule

• Product rule

• Chain rule

• Quotient rule

What is the derivative of the numerator in the expression one over cosine x?

• One

• Zero

• Sine x

• Negative one

What is the derivative of cosine x?

• Sine x

• Negative cosine x

• Negative sine x

• Cosine x

How is the expression simplified after finding the derivatives?

• By rewriting as a product of two fractions

• By dividing by sine x

• By adding sine x

• By multiplying by cosine x

What is the final form of the derivative of secant x?

• Secant x times tangent x

• Tangent x times sine x

• Cosine x times tangent x

• Secant x times sine x

What does sine x divided by cosine x equal?

• Cosecant x

• Secant x

• Tangent x

• Cotangent x

What is the purpose of rewriting the fraction as a product of two fractions?

• To simplify the expression

• To complicate the expression

• To change the expression

• To eliminate the expression