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Calculus

Derivatives

Concept Quizzes

Derivatives Warmup
Derivative by First Principle
Derivatives of Linear Functions
Derivatives of Polynomials
Derivatives of Rational Function
Derivatives of Exponential Functions
Derivatives of Logarithmic Functions
Derivatives of Trigonometric Functions
Instantaneous Rate of Change
Graphical Interpretation of Derivatives
Discrete First Derivatives Warmup

Challenge Quizzes

Derivatives: Level 2 Challenges

Derivatives Warmup

Let $f(x) = x^3 + x^2 + x + 1.$

What is the value of $f'(1)?$

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by Brilliant Staff

Let $n$ be a real number and $f(x) = x^n + x^{-n}.$

What is the value of $f'(1)?$

n

0

n + \frac{1}{n}

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by Brilliant Staff

Cameron is out running in a straight path for an hour. His distance (in kilometers) from home $t$ hours after leaving is given by the formula $s(t) = 12(t - t^2),\text{ for } 0 \leq t \leq 1.$

His average velocity for the hour-long run is 0 km./h., since

$\frac{s(1) - s(0)}{1-0} = \frac{0-0}{1-0} = 0.$

What is Cameron's average velocity (in km./h.) during the first half-hour of his trip?

0 3 6 9

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by Brilliant Staff

True or False?

For every quadratic function $f(x) = ax^2 + bx + c,$ there is a real number $x$ such that $f(x)=f'(x).$

True False

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by Brilliant Staff

True or False?

If $n$ is an odd integer and $f(x) = x^n,$ then $f'(x)$ is an even function, i.e. $f'(x) = f'(-x)$ for all $x$ in the domain of $f' .$

True False

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by Brilliant Staff