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differentiation - Review of the Method of Differentiation...

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Review of the Method of Differentiation Notes by C. Ho I The Basic Cases H Ð-Ñ œ ! H ÐB Ñ œ 8B B B 8 8" H Ð BÑ œ B H Ð BÑ œ  B H Ð BÑ œ B B B B # sin cos cos sin tan sec H Ð BÑ œ B B H Ð BÑ œ  B B H Ð BÑ œ  B B B B # sec sec tan csc csc cot cot csc H Ð/ Ñ œ / H Ð BÑ œ H Ð+ Ñ œ + + B B B B B B B " B ln ln II Algebraic Combinations H Ð-0ÐBÑÑ œ -H Ð0ÐBÑÑ B B H Ð0ÐBÑ „ 1ÐBÑÑ œ H 0ÐBÑ „ H 1ÐBÑ B B B H Ð0ÐBÑ † 1ÐBÑÑ œ ÐH 0ÐBÑÑ † 1ÐBÑ  0ÐBÑ † ÐH 1ÐBÑÑ B B B H œ B 0ÐBÑ 1ÐBÑ Š ÐH 0ÐBÑц1ÐBÑ0ÐBцÐH 1ÐBÑÑ Ð1ÐBÑÑ B B # III The Chain Rule If and are both differentiable and then 0 1 JÐBÑ œ 0Ð1ÐBÑÑß J ÐBÑ œ 0 Ð1ÐBÑÑ † 1 ÐBÑß w w w or if and are both differentiable, then C œ 0Ð?Ñ ? œ 1ÐBÑ .C .C .B .? .B .? œ IV Implicit Differentiation Differentiate both sides of the equation with respect to the independent variable and apply the Chain Rule for B
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