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## TOPICS

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**TOPICS**Derivative Theorems Theorem – 1 Theorem – 2 Theorem – 4 Theorem – 3 Examples Example - 1 Example - 4 Example - 2 Example - 5 Example - 3 Example - 6 Assessment**Theorem – 1:**Proof:**Theorem – 2:**Proof:**Theorem – 3:**Proof:**Theorem – 4:**Proof:**Example – 1:**Solution:**Example – 2:**Solution: Cont…**Example – 3:Differentiate log sin x by first principles.**Solution: Cont…**Example – 4:**Solution:**Example – 5:Differentiate the following function with**respect to x: Solution:**Example – 6:Differentiate the following function with**respect to x: Solution:**ASSESSMENT**Differentiate the following by first principles: I. e–x II. x2ex III. x sin x log x Differentiate the following with respect to x: I. x2ex log x • II. xnlogax ANSWERS**ANSWERS**Differentiate the following by first principles: • I. – e–x • II. (x2+ 2x )ex III. Differentiate the following with respect to x: • I. xex(1 + x log x + 2 log x) • II. xn –1(nlogax + 1/loga)