Derivatives of Trigonometric Functions

The video tutorial covers the derivatives of trigonometric functions, starting with sine and cosine, and extends to tangent, cotangent, secant, and cosecant. It explains the use of the product and quotient rules for differentiation and provides practice examples. The video also introduces the derivatives of inverse trigonometric functions, emphasizing the importance of memorizing these derivatives for solving problems and understanding integrals.

What is the derivative of sine x?

• Cosine x

• Sine x

• Negative sine x

• Negative cosine x

Which function is the derivative of cosine x?

• Cosine x

• Negative cosine x

• Sine x

• Negative sine x

What is the derivative of tangent x?

• Secant squared x

• Cosine squared x

• Sine squared x

• Cosecant squared x

Using the product rule, what is the derivative of x squared times sine x?

• x squared sine x + 2x cosine x

• 2x cosine x + x squared sine x

• 2x sine x + x squared cosine x

• x squared cosine x + 2x sine x

When using the quotient rule, what is the derivative of x over cosine x?

• Sine x minus x cosine x over sine squared x

• Sine x plus x cosine x over sine squared x

• Cosine x plus x sine x over cosine squared x

• Cosine x minus x sine x over cosine squared x

Which of the following is a derivative of an inverse trigonometric function?

• 1 over square root of 1 minus x squared

• 1 over x

• 1 over x squared

• 1 over x plus 1

Why is it important to memorize the derivatives of trigonometric functions?

• They are only used in algebra.

• They are not needed for differentiation.

• They are rarely used in calculus.

• They simplify the process of solving integrals.