Derivative Rules Practice
The three rules that differentiate almost everything: the product rule for multiplied chunks, the quotient rule for fractions, and the chain rule for functions inside functions. Master these and every derivative becomes bookkeeping.
1 Practice
Type your answer and press Check answer (or Enter). A wrong answer earns a hint; a second miss earns a stronger hint; a third miss walks you through the full solution. Scores and streaks are session-only.
2 What you’ll practice
Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.
Product rule
Differentiate (ax+b)(cx+d) and read off the linear result.
Quotient rule
Find the numerator of the derivative of (ax+b)/(cx+d).
Chain rule: powers
Peel (ax+b)^n into outer coefficient and new exponent.
Chain rule at a point
Evaluate a chained derivative at a given x.
Chain rule with trig
sin(ax), cos(ax) at special angles.
Product + chain combo
Both rules in one problem, evaluated at a point.
Spot the right rule
Multiple choice targeting the classic traps.
3 Watch out for these
The mistakes students make most often on these problems.
d/dx[(3x+1)^4] is 12(3x+1)³, not 4(3x+1)³. The chain rule always has two multiplications: outer′ × inner′.
It is low d-high MINUS high d-low. Reversing the order flips the sign of the whole derivative.
There is none: (fg)′ = f′g + fg′. Differentiating each factor and multiplying gives the wrong answer.