Differentiation Rules and Derivatives

This video tutorial covers the derivatives of trigonometric functions, including sine, cosine, tangent, cosecant, secant, and cotangent. It explains the application of these derivatives using the power, product, quotient, and chain rules. The video also provides examples and proofs to help understand the derivation of these functions, emphasizing the importance of memorizing key derivatives and recognizing patterns in trigonometric identities.

What is the derivative of sine x?

• Secant x

• Negative cosine x

• Cosine x

• Negative secant x

Which rule is used to find the derivative of a product of two functions?

• Quotient rule

• Chain rule

• Product rule

• Power rule

What is the derivative of x^3 using the power rule?

• 3x^2

• x^2

• 3x

• x^3

How do you find the derivative of a function divided by another function?

• Product rule

• Quotient rule

• Chain rule

• Power rule

What is the derivative of secant x?

• Negative secant squared x

• Secant x tangent x

• Negative secant x tangent x

• Secant squared x

Which rule is applied when differentiating a function inside another function?

• Power rule

• Product rule

• Chain rule

• Quotient rule

What is the derivative of cosine x?

• Negative cosine x

• Sine x

• Cosine x

• Negative sine x

What is the derivative of tangent x?

• Cosecant squared x

• Negative cosecant squared x

• Secant squared x

• Negative secant squared x

How can you express secant x in terms of cosine?

• 1/sine x

• Sine x

• Cosine x

• 1/cosine x

What is the derivative of cotangent x?

• Secant squared x

• Cosecant squared x

• Negative secant squared x

• Negative cosecant squared x