• Matéria: Matemática
  • Autor: matematicando
  • Perguntado 9 anos atrás

Seja r(x)=f(g(h(x))),onde:
h(1)=2;g(2)=3;h'(1)=4;g'(2)=5 e f'(3)=6 encontre e'(1)

Respostas

respondido por: andresccp
18
\Bmatrix{r(x)=f(g(h(x)))\\\\h(1)=2\\h'(1)=4\\ \\g(2)=3\\g'(2)=5\\\\f'(3)=6\end

e reescrevendo
f(x) = f\\\\g(x)=g\\\\h(x)=h

 utilizando a regra da cadeia

r(x) = f(g(h))\\\\r'(x)=f'(g(h))*g'(h)*h'\\\\\\\boxed{\boxed{r'(x)=f'(g(h(x)))*g'(h(x))*h'(x)}}

calculando r'(1)
r'(1)=f'(g(h(1)))*g'(h(1))*h'(1)}\\\\r'(1)=f'(g(2))*g'(2)*4\\\\r'(1)=f'(3)*5*4\\\\r'(1)=6*5*4=120
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