Trigonometric Derivatives and Identities

The video tutorial explains the derivatives of basic trigonometric functions, starting with sine and cosine. It then demonstrates how to find the derivative of tangent using the quotient rule, expressing tangent as sine over cosine. The tutorial continues with the derivative of cotangent, again using the quotient rule, and highlights the use of trigonometric identities to simplify results.

What is the derivative of sine with respect to x?

• Secant of x

• Tangent of x

• Negative sine of x

• Cosine of x

What is the derivative of cosine with respect to x?

• Sine of x

• Negative cosine of x

• Negative sine of x

• Tangent of x

Which rule is used to find the derivative of tangent?

• Quotient rule

• Product rule

• Chain rule

• Power rule

What is the derivative of tangent in terms of secant?

• Sine squared of x

• Cosine squared of x

• Secant squared of x

• Negative secant squared of x

What is the reciprocal of the tangent function?

• Sine

• Cosine

• Secant

• Cotangent

What is the derivative of secant in terms of trigonometric functions?

• Secant times cosine

• Secant times tangent

• Secant times cotangent

• Secant times sine

What is the relationship between secant and cosine?

• Secant is the derivative of cosine

• Secant is the square of cosine

• Secant is the integral of cosine

• Secant is the reciprocal of cosine

What is the derivative of cotangent with respect to x?

• Negative sine squared of x

• Negative cosine squared of x

• Negative cotangent squared of x

• Negative cosecant squared of x

Which identity is used to simplify the derivative of cotangent?

• Half angle identity

• Sum of angles identity

• Double angle identity

• Pythagorean identity

What is the derivative of cosecant in terms of trigonometric functions?

• Cosecant times tangent

• Cosecant times cosine

• Cosecant times cotangent

• Cosecant times sine