Derivatives on Product & Quotient Rule

Derivatives on Product & Quotient Rule

Assessment

Flashcard

Mathematics

12th Grade

Hard

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16 questions

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1.

FLASHCARD QUESTION

Front

What is the Product Rule for derivatives?

Back

If u(x) and v(x) are functions, then the derivative of their product is given by: (u*v)' = u'v + uv'.

2.

FLASHCARD QUESTION

Front

What is the Quotient Rule for derivatives?

Back

If u(x) and v(x) are functions, then the derivative of their quotient is given by: (u/v)' = (u'v - uv')/v^2.

3.

FLASHCARD QUESTION

Front

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

Back

g'(x) = (-3x^2 + 4x + 6)/(x^2 + 2)^2.

4.

FLASHCARD QUESTION

Front

Find the derivative of the function f(x) = x^3 + x^2 + 12.

Back

f'(x) = 3x^2 + 2x.

5.

FLASHCARD QUESTION

Front

What does it mean for the slope of the tangent line to be zero?

Back

The slope of the tangent line is zero at points where the function has a local maximum or minimum.

6.

FLASHCARD QUESTION

Front

How do you find the equation of the tangent line at a point?

Back

Use the point-slope form: y - f(a) = f'(a)(x - a), where a is the point of tangency.

7.

FLASHCARD QUESTION

Front

Find the tangent line to the curve y = \frac{12}{x^2} at x = 2.

Back

The tangent line is y = -3x + 9.

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