Derivatives of Trigonometric Functions

Professor Dave explains how to take derivatives of trigonometric functions, starting with sine and cosine, and then moving on to tangent, cotangent, secant, and cosecant. He uses graphical interpretations and mathematical rules like the product and quotient rules to derive these functions. The video also covers practice examples and briefly introduces the derivatives of inverse trigonometric functions.

What is the derivative of sine x?

• cosine x

• negative sine x

• secant x

• tangent x

At which points does the derivative of sine x equal zero?

• At all maxima and minima

• At all points where x is zero

• At all points where x is pi

• At all points where x is 2pi

What is the derivative of cosine x?

• tangent x

• negative sine x

• secant x

• sine x

Using the quotient rule, what is the derivative of tangent x?

• cosecant squared x

• secant squared x

• negative cosecant squared x

• negative secant squared x

What is the derivative of cotangent x?

• cosecant squared x

• negative cosecant squared x

• secant squared x

• negative secant squared x

What is the derivative of secant x?

• secant x tangent x

• negative cosecant x cotangent x

• cosecant x cotangent x

• negative secant x tangent x

In the product rule example, what is the derivative of (x squared) times (sine x)?

• (x squared)(cosine x) + (two x)(sine x)

• (two x)(sine x) + (x squared)(cosine x)

• (x squared)(sine x) + (two x)(cosine x)

• (two x)(cosine x) + (x squared)(sine x)

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

• Product rule

• Quotient rule

• Power rule

• Chain rule

What is a common form for the derivatives of inverse trigonometric functions?

• An expression involving x to the power of five

• One over an expression involving x squared

• One over an expression involving x cubed

• An expression involving x to the power of four

What should be memorized to differentiate functions with trigonometric terms effectively?

• Only the product and quotient rules

• Only the derivatives of the six trigonometric functions

• Derivatives of the six trigonometric functions and the product and quotient rules

• The chain rule and power rule