MathematicsHigh schoolEasy
Derivative from the definition
Find the derivative of a quadratic function using only the definition of the derivative.
Exercises
Exercises with solutions
Try on your own first. When you get stuck, reveal the hint, and at the end compare your solution with ours.
PhysicsPrimary schoolEasy
Distance in uniformly accelerated motion
A car starts from rest with constant acceleration. Find the distance it covers and its speed after a few seconds.
MathematicsHigh schoolMedium
Equation of the tangent line to a graph
Find the equation of the tangent line to the graph of a cubic function at a given point.
MathematicsHigh schoolMedium
Product rule and chain rule together
Differentiate x√(x² + 9) using the product rule and the chain rule, then work out the value of the derivative at x = 4.
MathematicsHigh schoolHard
Local extrema of a cubic function
Use the derivative to find the intervals where a function is increasing or decreasing and its local extrema.
MathematicsHigh schoolHard
Open box of maximum volume
Use the derivative to find what size of square to cut from each corner of a 30 cm × 48 cm sheet so that an open box has the largest volume.