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Derivative Rules Cheat Sheet
Six rules cover 95% of derivatives in a Calc I course: power, product, quotient, chain, and the standard derivatives of eˣ, ln(x), and the six trig functions. Once these are reflexive, the only real challenge is deciding which rule applies first.
When the method applies
- • Cannot remember which rule applies
- • Mixing up product rule and chain rule
- • Forgetting the inner derivative in chain rule
- • Cannot differentiate composite functions
Common mistakes
- • Mechanical memorisation without understanding
- • Rule application order confusion
- • Forgetting trig and exponential basics
Step-by-step method
- • Power rule: d/dx[xⁿ] = n·xⁿ⁻¹
- • Product rule: (uv)' = u'v + uv'
- • Quotient rule: (u/v)' = (u'v − uv') / v²
- • Chain rule: d/dx[f(g(x))] = f'(g(x))·g'(x)
- • d/dx[eˣ] = eˣ, d/dx[ln(x)] = 1/x, d/dx[sin(x)] = cos(x), d/dx[cos(x)] = -sin(x)
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Build long-term fluency
- • Drill 30 mixed derivatives daily for 2 weeks
- • Always identify the outermost function before chain rule
- • Write u and v explicitly when using product/quotient
Edge cases & deeper reading
For implicit differentiation, logarithmic differentiation, or partial derivatives, see the dedicated topic page — they extend these rules but add new mechanics.
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