f(t)=(√(1 +4T))
f(t)= (1 +4T)^1/2
f'(t)=1/2 (1 +4T)^-1/2.4
f'(t)=2 (1 +4T)^-1/2
f'(t)=2/ (1 +4T)^1/2
f'(t)=2/√ (1 +4T)
f'(t)=2(√(1 +4T))/(1+4t)
2*(1+4T)*(4)
à regrada cadeia simples, y = â(1 +4T) é o mesmo que y = (1 +4T)¹/ ²
y = u¹/ ²
dy/du = (1/2)*u -¹/²
u = 1 +4T
du/dT = 4 ......... dy/dT = dy/du * du/dT = (1/2) * u -¹/² * 4 = 2 * (1 +4T) -¹/²
................................ 2
Resposta. dy/dT = ---------------
............................ â(1 +4T)
.
(1+4t)^1/2
1/2(1+4t)^3/2
(1/2+2t)^3/2
^->sinal de elevadoo...
derivada voce 'desce' o expoente e subtrai menos 1
:D
(4 / 2*raiz quadrada (1 + 4T))
2 / raiz quadrada (1 + 4T).
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Verified answer
f(t)=(√(1 +4T))
f(t)= (1 +4T)^1/2
f'(t)=1/2 (1 +4T)^-1/2.4
f'(t)=2 (1 +4T)^-1/2
f'(t)=2/ (1 +4T)^1/2
f'(t)=2/√ (1 +4T)
f'(t)=2(√(1 +4T))/(1+4t)
2*(1+4T)*(4)
à regrada cadeia simples, y = â(1 +4T) é o mesmo que y = (1 +4T)¹/ ²
y = u¹/ ²
dy/du = (1/2)*u -¹/²
u = 1 +4T
du/dT = 4 ......... dy/dT = dy/du * du/dT = (1/2) * u -¹/² * 4 = 2 * (1 +4T) -¹/²
................................ 2
Resposta. dy/dT = ---------------
............................ â(1 +4T)
.
(1+4t)^1/2
1/2(1+4t)^3/2
(1/2+2t)^3/2
^->sinal de elevadoo...
derivada voce 'desce' o expoente e subtrai menos 1
:D
(4 / 2*raiz quadrada (1 + 4T))
2 / raiz quadrada (1 + 4T).