DIFFERENTIAL CALCULUS

By Q. MAKAU

USING THE ARITHMETIC OF DERIVATIVES - EXAMPLES DERIVATIVES OF EXPONENTIAL FUNCTIONS DERIVATIVES OF TRIGONOMETRIC FUNCTIONS ONE MORE TOOL - THE CHAIN RULE THE NATURAL LOGARITHM IMPLICIT DIFFERENTIATION INVERSE TRIGONOMETRIC FUNCTIONS THE MEAN VALUE THEOREM HIGHER ORDER DERIVATIVES VELOCITY AND ACCELERATION RELATED RATES CARBON DATING NEWTON’S LAW OF COOLING POPULATION GROWTH FURTHER PROBLEMS ZEROETH APPROXIMATION FIRST APPROXIMATION SECOND APPROXIMATION STILL BETTER APPROXIMATIONS SOME EXAMPLES ESTIMATING CHANGES AND ?X, ?Y NOTATION FURTHER EXAMPLES THE ERROR IN TAYLOR POLYNOMIAL APPROXIMATION LOCAL AND GLOBAL MAXIMA AND MINIMA FINDING GLOBAL MAXIMA AND MINIMA MAX/MIN EXAMPLES DOMAIN, INTERCEPTS AND ASYMPTOTES FIRST DERIVATIVE - INCREASING OR DECREASING SECOND DERIVATIVE - CONCAVITY SYMMETRIES A CHECKLIST FOR SKETCHING SKETCHING EXAMPLES L’HˆOPITAL’S RULE AND INDETERMINATE FORMS INTRODUCTION TO ANTIDERIVATIVES IV SOLUTIONS TO PROBLEMS DRAWING TANGENTS AND A FIRST LIMIT ANOTHER LIMIT AND COMPUTING VELOCITY THE LIMIT OF A FUNCTION CALCULATING LIMITS WITH LIMIT LAWS LIMITS AT IN?NITY CONTINUITY REVISITING TANGENT LINES DE?NITION OF THE DERIVATIVE INTERPRETATIONS OF THE DERIVATIVE ARITHMETIC OF DERIVATIVES - A DIFFERENTIATION TOOLBOX PROOFS OF THE ARITHMETIC OF DERIVATIVES