📚 Key Concepts
Limits and their meaningLeft and right hand limitsLimits at infinityContinuityDifferentiation basicsDerivative as rate of changeRules of differentiationDerivatives of standard functions
🎯 Key Formulas
Basic Derivative Rules:- d/dx(x^n) = nx^(n-1)
- d/dx(sinx) = cosx
- d/dx(cosx) = -sinx
- d/dx(e^x) = e^x
- d/dx(lnx) = 1/x
Chain Rule: d/dx[f(g(x))] = f'(g(x)) × g'(x)Product Rule: d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)Quotient Rule: d/dx[f(x)/g(x)] = [f'(x)g(x) - f(x)g'(x)]/[g(x)]²
⚠️ Common Mistakes to Avoid
Wrong application of limit rulesConfusion in indeterminate formsIncorrect derivative rules usageChain rule application errorsSign errors in derivativesForgetting quotient rule format
📖 Knowledge Prerequisites
FunctionsAlgebraTrigonometryBasic calculus concepts
💡 Tips for Students
Practice limit evaluation stepsRemember derivative rulesCheck continuity at pointsUse factorization for limitsUnderstand rate of change conceptMaster basic derivatives first
👉 Practice Recommedations
Evaluate simple limitsFind derivatives using rulesSolve practical rate problemsWork with composite functionsPractice chain ruleApply in maxima/minimaSolve tangent/normal problems
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