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# Differentiation

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Department
Mathematics
Course
MAT135H1
Professor
All Professors
Semester
Summer

Description
Differentiation/Derivatives:     Knowledge  Summary       Rules  for  differentiating:     Rule   𝒇 𝒙   𝒇′(𝒙)     Sum  rule:   𝑔 𝑥 + ℎ(𝑥)   𝑔′ 𝑥 + ℎ′(𝑥)     Constant  rule:   𝑐 ∗ 𝑓 𝑥   𝑐 ∗ 𝑓′(𝑥)     ▯ Product  rule:   𝑔 𝑥 ∗ ℎ(𝑥)   𝑔 𝑥 ∗ ℎ 𝑥 + 𝑔 𝑥 ∗ ℎ 𝑥     ▯ Quotient  rule:   𝑔 𝑥 𝑔 𝑥 ∗ ℎ 𝑥 − 𝑔 𝑥 ∗ ℎ 𝑥     ▯   ℎ(𝑥) ℎ 𝑥   Chain  rule:   ▯   𝑔 ℎ 𝑥   𝑔 ℎ 𝑥 ∗ ℎ′(𝑥)      Logarithm  differentiation  rules:     Rules  for  trigonometric  differentiation:       7.    sin  x  +  cos  x  =1       8.    1  +  cot  x=  csc  x   9.    cot  x=       ▯▯▯▯   10.    sin  2x=  2sinx  cosx     2 2   2 2   11.    cos  2x=  cos  x  –sin x=  2cos  x  -­‐1=  1-­‐  2sin x     12.    tan2x=   ▯  ▯▯▯▯   ▯▯▯▯▯ ▯ ▯   2 ▯▯▯▯▯ ▯ ▯ 13.    sin x=   ▯     2 ▯▯▯▯▯▯▯ 14.  cos  x=   ▯     Examples:                                                 (from  midterm  2010,  question  3)
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