Derivative of trig and in chain rule

The video tutorial covers the application of the chain rule in calculus, focusing on the derivative of the cosine function. It explains how to simplify derivative expressions and emphasizes the importance of understanding the cosine function as an operation rather than a multiplication. The tutorial also includes interactive elements to reinforce the learning process.

What is the derivative of the cosine function when using the chain rule?

• Negative cosine of the inside function

• Positive cosine of the inside function

• Negative sine of the inside function

• Positive sine of the inside function

What is the role of the inside function in the chain rule?

• It is ignored in the derivative process

• It is differentiated separately

• It is multiplied by the derivative of the outside function

• It is added to the derivative of the outside function

How do you simplify the expression 12x^2 / 4x^3?

• x

• x^3

• 3x

• 3x^3

What is the simplified form of the derivative Y' in the given example?

• 3 sin(ln(4x^3)) / x

• -3 cos(ln(4x^3)) / x

• -3 sin(ln(4x^3)) / x

• 3 cos(ln(4x^3)) / x

Why is it important to understand that cosine requires an argument?

• Because cosine without an argument makes no sense

• Because cosine is a multiplication operation

• Because cosine can be used as a standalone operation

• Because cosine is always positive