Test
Derivative fundamentals
This test introduces the derivative as a rate of change and applies the basic rules of differentiation. Tasks cover derivatives of constant, power, linear and quadratic functions.
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Question 1out of 10
Question 2out of 10
The average rate of change of a function on [a, b] shows the average change in the function value when x increases by one unit. Use:
(f(b) − f(a)) / (b − a).
First find the difference between the function values, then divide it by the interval length. Pay attention to the signs of negative numbers.
Question 3out of 10
Question 4out of 10
Question 5out of 10
Use the chain rule: ((kx + b)n)′ = n(kx + b)n−1 · k. First differentiate the function, then substitute the given value of x. Do not forget the factor k obtained by differentiating the inner function.
Question 6out of 10
Question 7out of 10
Use the product rule: (u · v)′ = u′v + uv′. Differentiate both linear factors, form the derivative expression, and only then substitute the given value of x. Do not simply multiply the derivatives of the two factors.
Question 8out of 10
Use the product rule: (u · v)′ = u′v + uv′. Differentiate both linear factors, form the derivative expression, and only then substitute the given value of x. Do not simply multiply the derivatives of the two factors.
Question 9out of 10
Question 10out of 10
Time left: 00:00:00
Sample questions
- Differentiate f(x) = ___x___.
- Find the value of the derivative of a composite power function at the given point.
- Find the value of the derivative of a product of two linear functions at the given point.
- For f(x) = ___x² + (___)x + (___), calculate f′(___).
- For f(x) = ___x² + (___)x, solve f′(x) = ___.
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