Cap3.Derivadas
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Transcript of Cap3.Derivadas
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3. DERIVADAS
Professora: Marcela Luciano Vilela de Souza
Tatiane da Silva Evangelista
Departamento de Matemática / ICENE
2º semestre / 2011
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3.1 A RETA TANGENTE E A DERIVADA
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DERIVADAS LATERAIS
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3.2 DERIVADA E CONTINUIDADE
Exemplo 3: f(x) = x2 se x 1
2 se x > 1
se f não é contínua,
então f não será
derivável
Lembre-se: a
recíproca do
Teorema NÃO vale.
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COMO PODE UMA FUNÇÃO DEIXAR DE SER DERIVÁVEL?
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3.3 REGRAS SOBRE DERIVAÇÃO
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3.4 DERIVADAS DE FUNÇÕES ELEMENTARES
1) Funções trigonométricas:
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2) Funções exponenciais:
f(x) = ax, a> 0 e a 1 f ‘(x) = ax ln a.
Caso especial:
f(x) = ex f ‘(x) = ex ln e = ex 1 = ex .
3) Funções logaritmicas:
f(x) = loga x, a > 0 e a 1 f ‘(x) =(1/x) loga e
Caso especial:
f(x) = ln x f ‘(x) =(1/x) ln e = (1/x) 1 = 1/x.
4) Funções inversas:
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3.5 DERIVAÇÃO IMPLÍCITA
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3.6 DERIVADAS DE ORDEM SUPERIOR
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3.7 APLICAÇÃO DA DERIVADA
Física: Movimento retilíneo
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3.8 TAXA DE VARIAÇÃO
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3.9 TAXAS RELACIONADAS
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