Constant Rule:
Derivative of a constant
function (or term) is ZERO.
Product Rule:
1𝑠𝑡 × 𝐷𝑒𝑟𝑖𝑣 2𝑛𝑑
+2𝑛𝑑 × 𝐷𝑒𝑟𝑖𝑣(1𝑠𝑡)
Power Rule:
Multiply by exponent and
reduce the exponent by 1.
Quotient Rule:
𝐿𝑂 𝑑𝐻𝐼 − (𝐻𝐼)(𝑑𝐿𝑂)
(𝐿𝑂)2
Constant Multiplier Rule:
Coefficients in the original
function remain, multiply
by the derivative.
Sine & Cosine Derivatives:
𝑑
sin 𝑥 = 𝑐𝑜𝑠𝑥
𝑑𝑥
𝑑
cos 𝑥 = − sin 𝑥
𝑑𝑥
All other trig functions can be
derived using sin/cos and
other derivative rules.
SIMPLIFY ALL FINAL DERIVATIVES FOLLOWING THESE GUIDELINES:
1. No negative exponents left in functions.
2. Combine like terms when present.
3. Simplify/reduce all fractions (numerical and algebraic cancelling).
4. No fractions inside fractions left in functions.
Sum/Difference Rule:
Break up multi-term
functions into individual
terms for separate
derivatives.
Horizontal Tangent Line:
Slope at a point (derivative) is
zero:
1. Take the derivative of the
function.
2. Set the derivative = 0 and
solve for x.