Differentiation Rules and Functions

The video tutorial begins with a review of derivatives, emphasizing the impact of constants on gradients. It then introduces the chain rule, explaining its use in simplifying complex derivatives without expansion. The quotient rule is discussed next, with a focus on differentiating fractions. Finally, the video covers graphing the sine function, highlighting intercepts and the range in radians.

What is the derivative of the function f(x) = x^2?

• 2x

• x^2

• x

• 2

What effect does a constant term have on the gradient of a function?

• It changes the y-intercept

• It changes the x-intercept

• It shifts the graph vertically

• It changes the gradient

Which rule is used to differentiate composite functions?

• Product Rule

• Quotient Rule

• Chain Rule

• Power Rule

What is the first step in applying the chain rule?

• Differentiate the outer function

• Differentiate the inner function

• Multiply by the derivative of the inner function

• Add the derivatives

What is the name of the rule used to differentiate a function that is a fraction?

• Power Rule

• Product Rule

• Quotient Rule

• Chain Rule

In the quotient rule, what is the expression for the denominator?

• v^2

• u^2

• uv

• u/v

What is a common mistake to avoid when simplifying expressions in the quotient rule?

• Adding instead of subtracting

• Misplacing the negative sign

• Ignoring the numerator

• Forgetting to square the denominator

What happens to the x terms in the numerator when simplifying the expression in the quotient rule?

• They divide

• They multiply

• They add up

• They cancel out

What is the range of the sine function?

• -π to π

• 0 to 2π

• -1 to 1

• 0 to 1

What are the units of angles when graphing the sine function from 0 to 2π?

• Radians

• Turns

• Degrees

• Gradians