1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ [๐๐ข] = ๐๐ข′ 20) [๐ข ± ๐ฃ] = ๐ข′ + ๐ฃ′ 21) [๐ข๐ฃ ] = ๐ข๐ฃ′ + ๐ฃ๐ข′ 22) ๐ข [ ]= ๐ฃ๐ข′ −๐ข๐ฃ′ ๐๐ฅ ๐ฃ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ 23) ๐ฃ2 [๐ ] = 0 24) [๐ข๐ ] = ๐๐ข๐−1 ๐ข′ 25) [๐ฅ ] = 1 26) [|๐ข|] = [๐๐๐ข] = ๐ข |๐ข| (๐ข ′ ), ๐ข ≠ 0 27) ๐ข′ 28) ๐ข [๐ ๐ข ] = ๐ ๐ข ๐ข′ [๐๐๐๐ ๐ข] = 29) ๐ข′ 30) (๐๐๐)๐ข [๐๐ข ] = (๐๐๐)๐๐ข ๐ข′ 31) [sin ๐ข] = (cos ๐ข)๐ข′ 32) [cos ๐ข] = −(sin ๐ข)๐ข′ 33) [tan ๐ข] = (๐ ๐๐ 2 ๐ข)๐ข′ 34) [cot ๐ข] = −(๐๐ ๐ 2 ๐ข)๐ข′ 35) [sec ๐ข ] = (sec ๐ข tan ๐ข)๐ข′ 36) [csc ๐ข ] = −(csc ๐ข cot ๐ข)๐ข′ 37) [arcsin ๐ข] = ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ ๐ ๐๐ฅ −๐ข′ [arccos ๐ข] = √1−๐ข2 ๐ข′ [arctan ๐ข] = [arccot ๐ข] = 1+๐ข2 −๐ข′ 1+๐ข2 ๐ข′ [arcsec ๐ข] = [arccsc ๐ข] = |๐ข|√๐ข2 −1 −๐ข′ |๐ข|√๐ข2 −1 [sinh ๐ข] = (cosh ๐ข)๐ข′ [cosh ๐ข] = (sinh ๐ข)๐ข′ [tanh ๐ข] = (๐ ๐๐โ2 ๐ข)๐ข′ [coth ๐ข] = −( ๐๐ ๐โ2 ๐ข)๐ข′ [sech ๐ข] = −(sech ๐ข tanh ๐ข)๐ข′ [csch ๐ข] = −(csch ๐ข coth ๐ข)๐ข′ [๐ ๐๐โ−1 ๐ข] = [๐๐๐ โ−1 ๐ข] = [๐ก๐๐โ−1 ๐ข] = [๐๐๐กโ−1 ๐ข] = [๐๐๐ โ−1 ๐ข] = [๐ ๐๐โ−1 ๐ข] = [๐๐ ๐โ−1 ๐ข] = ๐ข′ √๐ข2 +1 ๐ข′ √๐ข2 −1 ๐ข′ 1−๐ข2 ๐ข′ 1−๐ข2 ๐ข′ √๐ข2 −1 −๐ข′ ๐ข√1−๐ข2 ๐ข′ |๐ข|√1+๐ข2 ๐ข′ √1−๐ข2 Source: Calculus 10th Edition (Ron Larson and Bruce Edwards) Tecson, Ameg G. - Reviewer Tecson, Ameg G. - Reviewer