Derivatives of Trigonometric Functions

The video tutorial covers the derivatives of six trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant. It highlights patterns in these derivatives, particularly the negative sign for cofunctions starting with 'c'. The tutorial provides examples to demonstrate how to calculate derivatives of expressions involving these functions, emphasizing the importance of recognizing patterns to simplify the process.

What is the derivative of sine x?

• cosine x

• negative sine x

• secant x

• cosecant x

Which trigonometric function's derivative is negative sine x?

• secant x

• tangent x

• cosine x

• sine x

What is the derivative of tangent x?

• negative secant squared x

• secant squared x

• cosecant squared x

• negative cosecant squared x

The derivative of cotangent x is similar to which function?

• secant squared x

• negative cosecant squared x

• cosecant x

• negative secant x

In the expression 5 sine x - 4 tangent x, what is the derivative of tangent x?

• negative sine x

• cosecant squared x

• cosine x

• secant squared x

What is the derivative of secant x?

• negative secant x

• negative cosecant x

• secant x tangent x

• cosecant x

In the expression 8 secant x - 5 cosine x, what is the derivative of cosine x?

• secant x

• negative sine x

• negative secant x

• sine x

What is the derivative of cotangent x?

• negative secant squared x

• cosecant squared x

• negative cosecant squared x

• secant squared x

The derivative of cosecant x involves which two functions?

• tangent and cotangent

• cosecant and cotangent

• secant and tangent

• sine and cosine

If you know the derivatives of sine, tangent, and secant, what can you deduce?

• The derivatives of all trigonometric functions

• The derivatives of only tangent and cotangent

• The derivatives of their cofunctions

• The derivatives of only sine and cosine