FOURTH QUARTER MATH 11 REVIEWER

What is the derivative of a constant function f(x)=c?

• c

• 0

• d

• 1

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

• nx^(n-1)

• c

• n^x

• d

What is the derivative of fx=5x^3.

• 15x

• b. 15x^3

• 15x^2

• 15

What does the Chain Rule help to differentiate?

• A sum of two functions

• A product of two functions

• A quotient of two functions

• A composite function

What is the derivative of fx=(3x+2)^5 using the Chain Rule?

• 5(3x+2)^3∙2

• 5(3x+2)^4∙3

• 5(3x+2)^4∙3

• 5(3x+2)^3∙3

What is the derivative of hx=(x^3+2x)^5.

• 5(x^3+2x)^4

• 5(x^3+2x)^4∙(3x^2+2)

• 5(x^3+2x)^5∙(3x^2+2)

• 5(x^3+2x)^3∙(3x^2+2)

Why is the Quotient Rule necessary when differentiating a fraction instead of applying the Power Rule or Product Rule?

• Because fractions follow different algebraic rules, requiring a unique differentiation formula.

• Because division is not directly differentiable, so subtraction must be used instead.

• Because the derivative of a quotient depends on both the numerator and denominator, requiring a structured formula.

• Because applying the Power Rule alone would lead to an incorrect result when differentiating a fraction.

Which of the following best illustrates why the Chain Rule is necessary when differentiating composite functions?

• Because composite functions involve multiple variables, requiring the differentiation of each part separately.

• Because differentiation is distributive, allowing us to differentiate the inner and outer functions separately.

• Because the Chain Rule ensures that the derivative of a composition accounts for the rate of change of the inner function.

• Because applying the Power Rule directly to composite functions always gives the correct result.

Given the function: fx=(3x^2+5x)^4. Which differentiation rule should be applied first to compute f'x.

• Power Rule

• Product Rule

• Chain Rule

• Quotient Rule

Find the derivative of the function: f(x)=(5x^3−2x+4)^7. Which of the following is the correct first step in applying the Chain Rule?

• Multiply the exponent by the coefficient inside the parentheses and subtract 1 from the exponent.

• Differentiate the inner function 5x^3−2x+4 separately and multiply by the derivative of the outer function.

• Expand the function using the Binomial Theorem before differentiating term by term.

• Apply the Product Rule since there are multiple terms inside the parentheses.