Unit 5 WU: Day 3 (Calculus)

Front

What is the quotient rule in calculus?

Back

The quotient rule states that if you have a function v = f/g, then the derivative v' is given by (vu' - uv')/v².

Front

How do you find the derivative of a function that is a quotient of two functions?

Back

To find the derivative of a function that is a quotient, apply the quotient rule: v' = (f'g - fg')/g².

Front

What is the derivative of y(x) = (4x² + 3)/(2x² - 5)?

Back

y' = -52x/(2x² - 5)².

Front

What is the derivative of g(x) = (3x - 2)/(x² + 2)?

Back

g' = (-3x² + 4x + 6)/(x² + 2)².

Front

Given f(2) = 3, g(2) = -3, f'(2) = 5, and g'(2) = 1, what is v'(2) if v = f/g?

Back

v'(2) = -2.

Front

What is the general formula for the derivative of a quotient of two functions?

Back

If v = f/g, then v' = (f'g - fg')/g².

Front

What is the significance of the derivative in calculus?

Back

The derivative represents the rate of change of a function with respect to its variable.

Front

How do you apply the quotient rule to find the derivative of a function?

Back

Identify f and g, compute f' and g', then substitute into the quotient rule formula.

Front

What is the first step in finding the derivative of a quotient?

Back

Identify the numerator function f and the denominator function g.

Front

What does the notation f'(x) represent?

Back

f'(x) represents the derivative of the function f with respect to x.