Derivatives and Chain Rule Concepts

The video tutorial from Excellence Academy covers the differentiation of trigonometric functions, focusing on sine, cosine, and related functions. It provides a table of derivatives and demonstrates the application of the chain rule through four examples, including differentiating sine of log x, cosecant of exponential, sine of a sum involving exponential, and cosine cubed. The tutorial emphasizes the importance of recognizing when to use the chain rule and notes that differentiating functions starting with 'c' often results in a negative outcome.

What is the derivative of sin(x)?

• sec^2(x)

• -cosec^2(x)

• -sin(x)

• cos(x)

What is the derivative of cos(x)?

• tan(x)

• -sin(x)

• sin(x)

• sec(x)

What is the derivative of tan(x)?

• cosec^2(x)

• sec^2(x)

• -sec^2(x)

• -cosec^2(x)

What is the derivative of sec(x)?

• -cosec(x)cot(x)

• cosec(x)cot(x)

• -sec(x)tan(x)

• sec(x)tan(x)

What is the derivative of cot(x)?

• -sec^2(x)

• cosec^2(x)

• -cosec^2(x)

• sec^2(x)

What is the derivative of cosec(x)?

• sec(x)tan(x)

• -cosec(x)cot(x)

• -sec(x)tan(x)

• cosec(x)cot(x)

In the chain rule, if y = sin(u) and u = log(x), what is dy/du?

• -cos(u)

• sec(u)

• -sin(u)

• cos(u)

In the chain rule, if u = log(x), what is du/dx?

• log(x)

• x

• 1/x

• 1

What is the final derivative of y = sin(log x) with respect to x?

• sin(log x)/x

• -cos(log x)/x

• -sin(log x)/x

• cos(log x)/x

In Example 2, what is the first step in using the chain rule for y = cosec(3e^(2x))?

• Let u = e^(2x)

• Let u = 3x

• Let u = 3e^(2x)

• Let u = 2x