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· tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du...

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Page 1: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 2: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 3: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 4: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 5: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 6: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 7: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 8: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 9: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 10: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 11: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 12: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 13: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 14: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 15: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 16: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 17: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 18: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 19: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 20: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 21: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

Page 22: · tanhu = sech2 u dx Proof: d tanh u — dx dx dx Sinh u cosh u dx dx du sinhu dx du dx du du cosh u — sinhu dx cosh2 u du = sech2 u dx (cosh2 u — sinh2 u) dx cosh2 u cosh2

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