Unit 2 · 6 lessons

Derivative Rules

Stop taking limits by hand: the power, sum, product, chain and quotient rules, then the derivatives of sine, cosine, eˣ and aˣ, so any function in the course can be differentiated in a few lines.

57 practice questions
40 flashcards
3 interactive lessons

Start lesson 1 →Unit 2 test review →

Lessons

1Power, Constant, Sum and Difference RulesFirst principles works, but it is slow. A handful of patterns (the power rule plus the constant, constant multiple, sum and difference rules) let you differentiate any polynomial, and any sum of powers of x, in one line.Interactive10 questions
2The Product RuleThe derivative of a product is NOT the product of the derivatives. The product rule, f′g + fg′, comes straight from a growing rectangle, and it handles products you could never expand.8 questions
3The Chain RuleFor a function inside a function, rates multiply: the derivative is the rate of the outer function times the rate of the inner one. The chain rule handles powers of polynomials and radical functions without expanding anything.9 questions
4Derivatives of Rational FunctionsA quotient can be differentiated two ways: rewrite it as a product with a negative exponent and use the product and chain rules, or use the quotient rule directly. Both give the same answer.9 questions
5Derivatives of Sine and CosineRead the slopes off the sine curve and you get the cosine curve; read the slopes off cosine and you get negative sine. With x in radians, these two facts plus the chain, product and quotient rules differentiate any sinusoidal model.Interactive10 questions
6Derivatives of Exponential FunctionsThe slope of an exponential curve is always proportional to its height. For one special base, e ≈ 2.718, the slope equals the height exactly, so the derivative of $e^{x}$ is $e^{x}$ ; every other base picks up a factor of $ln a$ .Interactive11 questions