Understanding the Derivative of Cosecant Function

The video tutorial demonstrates the process of finding the derivative of cosecant x with respect to x. It begins by using a reciprocal identity to express cosecant x as 1/sin x. The quotient rule is then applied to find the derivative of 1/sin x. The tutorial simplifies the expression step-by-step, ultimately arriving at the derivative: negative cosecant x times cotangent x. The explanation includes rewriting the expression as a product of two fractions and identifying the final derivative expression.

What identity is used to express cosecant x in terms of sine x?

• Pythagorean identity

• Reciprocal identity

• Quotient identity

• Product identity

Which rule is applied to find the derivative of 1/sinx?

• Power rule

• Chain rule

• Product rule

• Quotient rule

What is the derivative of the numerator in the quotient rule application?

• sin x

• 1

• cos x

• 0

How is the denominator sin x^2 rewritten during simplification?

• sin x^2

• sin^2 x

• 2sin x

• cos^2 x

What is the simplified form of the derivative after applying the quotient rule?

• cos x / sin^2 x

• sin x / cos x

• cos x / sin x

• 1 / sin x

How is the expression -1/sinx * cosx/sinx related to trigonometric functions?

• It represents secant and tangent

• It represents sine and cosine

• It represents tangent and cotangent

• It represents cosecant and cotangent

What is the final expression for the derivative of cosecant x?

• secant x * cotangent x

• cosecant x * tangent x

• cosecant x * cotangent x

• secant x * tangent x

Which trigonometric function is equivalent to 1/sinx?

• Cosecant x

• Cotangent x

• Tangent x

• Secant x