4.2.2 The Quotient Rule Flashcards Preview

AP Calculus AB > 4.2.2 The Quotient Rule > Flashcards

Flashcards in 4.2.2 The Quotient Rule Deck (9):
1

The Quotient Rule

• Similar to the product rule, the derivative of a quotient of two functions is not necessarily equal to the quotient of the derivatives.
• The quotient rule states that if q(x) = f(x)/g(x), where f and g are differentiable functions, then q is differentiable except where g(x)=0 and q'(x) = g(x)f'(x)-f(x)g'(x) / [g(x)]^2

2

note

- The derivative of a quotient of two functions is not necessarily equal to the quotient of the derivatives.
- Much like the product rule, there is a shortcut you can use to find the derivative of a quotient. The shortcut is called the quotient rule.
- Try to remember this chant when using the quotient rule.
- Here is the formula for the quotient rule.
- To use the quotient rule you will need to find the derivative of the numerator and the denominator. Then just combine the different pieces according to the chant.
- Combining terms and canceling can often simplify the result.
- Here is another example of the quotient rule.
- Multiply the denominator by the derivative of the numerator, subtract the numerator multiplied by the derivative of the denominator, and divide everything by the denominator squared.

3

Find the derivative.f(x)=(x−2)/x^2

f′(x)=−x+4/x^3

4

Suppose f(x)=x^2−3x+2 / 2x+1. What is the equation of the line tangent to f at the point (0,2)?

y = −7x + 2

5

What is the equation of the line tangent to f at the point (2, 1)?
f(x)=x^2−3 / 2x−3

y = 2x − 3

6

Find the derivative.f(x)=x^2+1/x+1

f′(x)=(x+1)(2x)−(x^2+1) /(x+1)^2

7

Find the derivative of:g(x)=2x^2+3x / x−3x^2+2.

g'(x)=11x^2+8x+6( / x−3x2+2)^2

8

Find the derivative of:h(x)=x^3+3x+4 / x^3+3x−2.

h'(x)=−18x^2−18 / (x^3+3x−2)^2

9

Find the derivative.f(x)=x+3/x

f′(x)=−3/x^2

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